When it comes to modding, Skyrim is possibly one of the best examples how the fans and community can improve and update on a game and make it better to what was released or even stay relevant after years.

Mods and fan-fixes improve and extend functionality, content, quality and polish performance or plain out fix bugs that the developer didn't.
Thus keeping with the times. Skyrim with his many extensions, additional content and picture quality mods still looks up-to date and is one of the most open and immersive worlds in which even NPC's (non-player-characters) have a live and career for themselves through mods.
Fans over time created the game they ever wished for and that the developer could never deliver.

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So, what do you need to be able to mod?
Let's go through some few points here:

0.) Skyrim game version and release history:
To get more clarification over the different game versions and version names, here some basic understanding.
Skyrim released first on 11th November 2011 as "Skyrim". Over time new content via seperate AddOn extension like "Dawnfguard", "Hearthfire" and "Dragonborn".
On 4th of June 2013 Bethesda released a complete version called "Skyrim Legendary Edition" in which it bundled in all the extended content, that became a new baseline for modders - nowadays you might come accross the term "Oldrim" for this.
On 28th of October 2016 Bethesda re-released an overhaul version of the game with some slight graphical improvements, some engine recode to bring the engine to handle 64 bit address space and such - that's what is called "Skyrim Special Edition". Some might call it "remaster" but Bethesda themselves was very careful to warn it is NOT a remastered version. Yet the new 64bit code broke many of the countless existing mods, so people stuck with the LE version at first until their favorite mods were ported over. SSE then slowly became the new baseline.
On 4th of October 2017 Bethesda released its Creation Club via patch onto many of it's games. The Creation Club should make available approved mods from the Modding Community made available via purchase.
As part of Skyrims 10 year anniversary, Bethesda ingeniously thought of re-re-releasing the game as an "Anniversary Addition" in November 2021 in which it bundled many of it's Creation Club mods in one DLC.

1.) The Anniversary Addition:
Know that the so called Anniversary Edition does nothing but introduce the notorious Creation Club store to the game and bundles in some of its content. A store that was implemented to market some of the many fan created mods. Mods from modders that Bethesda approved. The Anniversary Edition uses that store and bundles in 74 of it's items and fan-made quest that you would otherwise need to pay for in the Creation Club

But what about other mods?
Nope, the Anniversary Edition will only bring the game to the latest iteration and bundle in some selected Creation Club mods. Thus constantly breaking other mods or make your life hard to impossible to run or implement them by any other means than the Creation Club.
So what is the solution here? -> see 2.)

Be aware that on GoG, the Anniversary Edition doesn't even introduce the Creation Club into the game were you can buy mods (a good thing in my opinion). It is mainly just a DLC (downloadable content) that bundles some mods: you "only" get your game updated to the latest version with Bethesda's sometimes mod-breaking tweaks (already true for the SSE) and a pack of selected mods from the Creation Club to make use of some graphical improvements. For Console gamers that have no means of modding or say in what version they want to run or very new-to-Skyrim players that are not yet into modding , this might be a comfort option to get at least some graphical revamps with their first install.

Ultimately, you don't need the Anniversary Edition. It does not deliver any better game or content than the Special Edition does. The Special Edition gives you all you need at its latest updated version and will give you much more freedom to create the Skyrim YOU want.

My advice: for now, hold of on buying or updating via DLC to the Anniversary Edition. (This may also change over time as many more version updates and the Creation Club DLC content will surely make this a new baseline over time. Maybe in 1 or 2 years the Anniversary Edition DLC is worth it and can be grabbed for cheap)
But if you do, not all is lost, the magic word is "downgrading" (see below).

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2.) The Special Edition:
After the previous Legendary Edition that included all the extensions and AddOns into one came an overhaul and graphic cleanup of sorts that culminated in the so called Skyrim Special Edition (or SSE). An important feature that SSE brings is an engine rework that introduces 64bit. The community adapted and many of the previous mods have been ported over over time to also work under SSE.
You can regard SSE as the most recent and polished version that offers today almost all of the relevant mods.
If you are serious about modding Skyrim - and sooner or later you will get there - get the SSE, the Anniversary Edition mod pack from the Creation Club is not needed.
The latter is unnecessary handcuffs and money extortion.

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3.) Which Game version is good for modding?
As of today, the SSE is version wise on par with the latest Anniversary Edition patches and sits at game version 1.6.659.0.8. The Anniversary Edition is currently basically the latest patched Special Edition plus a mod-bundle of Creation Club purchasable mods.
However, not all mods are that up to date and run with that most recent game version. For compatibility with many and most mods, the game version 1.5.97 is recommended as of now (may change over time).
Basically you want to be able to run SKSE64 and the mods you wish.
GoG and many other Stores don't offer a downgrade option to that slightly older version.
So to solve the puzzle, the community has come up with yet another quality service and mod: meet the "unofficial Skyrim Special Edition Downgrade patcher" (can be found on Nexus Mods).
For Steam there also exists an "unofficial Skyrim downloader" that can install older game versions from the Steam repositories. For the GoG version, the Downgrade patcher is currently the only possibility for you to downgrade to a more largely supported game version.

To manage all the mods from Nexus Mods or other sources some people like to use Mod Managers like "Vortex". The latest version of Vortex v1.6.13 should already support the GoG game version.

These are the perils you are facing: while strictly purely graphical mods may run with the latest patched version and the Anniversary content, many of the other beautiful mods and mechanics might not work immediately with Bethesda's game changes and tweaks.
And let's be honest for a second: Bethesda is not a good company to deliver quality and performance. The game was outdated when it arrived, the engine was old and did things in bad ways that recent engines already did better 10, 11, 12 years ago and they never fixed the many bugs, even today - they were very careful to not call their re-vamps "remasters". Bethesda games are hardware hogs and ill polished (take Fallout for another example). So why would you go with how Bethesda intended their game to be and only use what was "approved by them" for a game that is 10 years old now and was never technically state of the art?
In my opinion, you shouldn't have to.
It's an over 10 year old game with many short comings - graphically, in game mechanics and bug/Performance wise. That is were the modding community comes in and improves the game in many different aspects, be it graphic overhauls or total new game mechanics like physically moving grass, combat, survival mechanics, or NPC's that have their own conversations (see e.g. Citizens of Tamriel, Immersive Citizens AI Overhaul or other mods), decision paths and day cycles (to name but a few). With mods Skyrim can look and feel up to date even compared to modern games.
Sooner or later you will want to mod your game - some may even go as far to say a modded Skyrim is the only Skyrim you still want to play today because the Vanilla Skyrim is just ... old and clonky.

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4.) And what about Linux?
SSE and it's mods install and run fine through the means of Wine, Wine GE, Proton, Proton Ge and the like.

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5.) So what Mods should I get?
Uff, there are so many and constantly new ones. It is totally up to you. To get an overview of good and essential mods that you might want, you need to study and research. Start with looking at recommendations and modlists by other people suggested on Reddit or Youtube.
Nexus Mods is a good initial address for mods. There might be others like LoversLabs for more "erotic" content.

But one mod that can be regarded as essential in any case is the "unofficial Skyrim Speial Edition Patch" (USSEP). It fixes all the bugs and crashes that Bethesda hasn't managed to fix in their 10 years of Skyrim, patches, re-releases and overhauls to this day.

Regarding section 3, "For Steam there even exists a "unofficial Skyrim downloader" ", that function used by the described mod is available in Steam, but access to prior versions has been blocked by Bethesda, so it is no longer possible to select older versions in that way. Differently stated, one can access multiple versions of many Steam games, but only when the publisher allows such access or even provides multiple versions.

For example, there is more than one accessible version for Rise of the Tomb Raider and Resident Evil 2 (remake), but only one version of SE and Bioshock.

If you're not into random fan mods with questionable continuity then I think the Anniversary Edition is quite nice. Everything in it is approved by Bethesda, and on the wiki, and therefore is official in every meaningful sense. It all feels right lore wise, and after the AE update it's all found in the world by finding notes and asking for jobs, which means it doesn't stand out as a "mod."

If you're a big modder who is always trying out new items and quests from Nexus then yeah, maybe the AE seems silly, but for the many, MANY people who don't do that I think the AE is easily worth the price. Lots of cool and official content.

Also no developer or publisher should refrain from updating their game because of mods.

Thank you, I wasn't aware of this. I edited the article following your feedback.

The Anniversary Edition only adds the CC mods. There is no CC to buy from in this version (and in fact, Bethesda is killing it after it was mostly a failure, if what I've read elsewhere is to be believed). If one wants access to those mods, there is literally no reason not to buy the Anniversary edition, as the game is exactly the same with a separate "DLC" for those mods. Neither version here has easy access to mods, though Wrye Bash and Bain should still work for them (my chosen mod manager way back in the day). MO2 should be compatible any time now, and that's great.

Wrye Bash is being updated to work with the GOG version, but currently doesn't.

I see Bash on Nexus is uploaded by... someone. Does Wrye no longer code Bash? I had some great conversations with him back in the day. He was very.. particular about what to add to Mash and Bash.

Thanks for the info. Never actually had the chance to play it and I shall think about it while the sale is still on.

Skyrim mods list Guide: How to AUTO install 350+ Graphics Overhaul mods

https://www.youtube.com/watch?v=hsgTI7iTE1E

So MO2 does not currently work with the GOG version then? According to the Sticky post from that channel owner at the top of the comments section which he posted 2 days ago, that mod list is no longer working with the current version of the game (that being the version which all GOG users are forced to use since no prior version is available on GOG) because Bethesda recently updated the game but not all of the mod makers whose mods on that list have updated their mods.

Maybe it is good to clarify for readers new to modding what MO2 is.
For those not into Skyrim Modding the past 8 years ... MO2 is yet another Mod Manager called ... wait for it ... "Mod Organizer 2".

(I hate introducing abbreviations outright - how is anyone supposed to know what this means? ;) )

Thanks for the info. I'll get the Special Edition in time then instead of the Anniversary Edition.

It's possible to mod Skyrim SE (GOG) manually without a client / mod manager, ie, install mods from a local backup drive to retain 100% offline functionality. You need to:-

1. Add mods to the game_install\data subfolder, ie, unzip them into there after manually downloading them from Nexus.

2. The file the game uses to "see" the mods is called %LOCALAPPDATA%\Skyrim Special Edition GOG\plugins.txt and you need to include the names of each .esp filenames of the mods you added and arrange correct load order.

3. Non-updated mod utilities designed for Steam (eg, Nexus Mod Manager / Vortex), may mistakenly look for the file in "%LOCALAPPDATA%\Skyrim Special Edition" where Steam installs it. You may need to copy / move this to "%LOCALAPPDATA%\Skyrim Special Edition GOG" for the game to see it.

4. For SKSE, use the file called "Current GOG Anniversary Edition build 2.2.2 (game version 1.6.659)" from here. You would unzip this into the main game_install folder (ie, place skse64_1_6_659.dll & skse64_loader.exe next to SkyrimSE.exe rather than in the data subfolder) then run skse64_loader.exe.

For those who hate clients / mod managers, in reality nothing has really changed about how the core mechanics of Creation Engine mods work, ie, the game will look for "%LOCALAPPDATA%\Skyrim Special Edition GOG\plugins.txt" file, then read the mentioned .esp mod filenames from its install_folder\data subfolder, the same way Oblivion functions (which stores its mod load order in "%LOCALAPPDATA%\Oblivion\plugins.txt").

There is only one version on GOG. It is the Special Edition (1.6.xx) and the Anniversary Upgrade is only several Creation Club mods as a DLC. The Anniversary Edition on GOG is the Special Edition + the Anniversary Creation Club DLC.