what mods are essentially for the best FO4 experience?

For your first playthrough I'd only recommend these:

Extended Dialogue Interface
nexusmods.com/fallout4/mods/27216

Use these if you're planning to use the settlement system:

Scrap Everything
nexusmods.com/fallout4/mods/5320

Place Everywhere
nexusmods.com/fallout4/mods/9424

Settlements - Lights Out
nexusmods.com/fallout4/mods/15810

and to make it feel more like classic Fallout:

Pip Boy 2000
nexusmods.com/fallout4/mods/32025

Dynamic Music Overhaul (used to disable the combat music)
nexusmods.com/fallout4/mods/10370

Classic Fallout Ambient Music
nexusmods.com/fallout4/mods/2990

Fallout 3/New Vegas Feral Ghouls Replacer
nexusmods.com/fallout4/mods/39290

Slower Ghouls
nexusmods.com/fallout4/mods/13289

LevelUpMenuEx (replaces the perk poster)
nexusmods.com/fallout4/mods/28822

Be Exceptional - Skills and Perk Overhaul (restores Skills)
nexusmods.com/fallout4/mods/28222

Start Me Up - Alternate Start and Dialogue Overhaul (allows you to role play again)
nexusmods.com/fallout4/mods/18946

You will need F4SE (Fallout 4 Script Extender) for most of these mods

Bugfixes and Essentials:
- Fallout 4 Script Extender (F4SE) (https://f4se.silverlock.org/)
- Address Library for F4SE Plugins (https://www.nexusmods.com/fallout4/mods/47327)
- Buffout 4 (https://www.nexusmods.com/fallout4/mods/47359)
- Baka ScrapHeap - Script Memory Limit Expander (https://www.nexusmods.com/fallout4/mods/46340)
- High FPS Physics Fix (High FPS Physics Fix) (https://www.nexusmods.com/fallout4/mods/44798)
- Rusty Face Fix (https://www.nexusmods.com/fallout4/mods/31028)
- Shadow Boost FO4 (https://www.nexusmods.com/fallout4/mods/63482)
- Interior NavCut Fix (https://www.nexusmods.com/fallout4/mods/72904)
- Unofficial Fallout 4 Patch (https://www.nexusmods.com/fallout4/mods/4598)

Only for RTX-GPUs with enabled weapon debris
- Weapon Debris Crash Fix (https://www.nexusmods.com/fallout4/mods/48078)

Must Haves:
- Mod Configuration Menu (https://www.nexusmods.com/fallout4/mods/21497)
- Extended Dialogue Interface (https://www.nexusmods.com/fallout4/mods/27216)
- Backpacks of the Commonwealth (https://www.nexusmods.com/fallout4/mods/29447)
- Automatically Lowered Weapons (https://www.nexusmods.com/fallout4/mods/20093)
- Laser weapons 1st person reposition (https://www.nexusmods.com/fallout4/mods/23102)
- Fill'em Up Again (https://www.nexusmods.com/fallout4/mods/12674)
- Crafting Highlight Fix (https://www.nexusmods.com/fallout4/mods/27479)
- QuickTrade Redux (https://www.nexusmods.com/fallout4/mods/41101)
- New Equipment Overhaul (NEO) (https://www.nexusmods.com/fallout4/mods/65761)
- Remove Weapon Mods (https://www.nexusmods.com/fallout4/mods/10267)
- See Through Scopes (https://www.nexusmods.com/fallout4/mods/9476)
- Uneducated Shooter - QE Leaning and Gun Inertia (https://www.nexusmods.com/fallout4/mods/56789)
- Professional Ammo Crafting (P.A.C) (https://www.nexusmods.com/fallout4/mods/22175)
- MJC Dogmeat AI Tweak (https://www.nexusmods.com/fallout4/mods/37584)
(with this mod Dogmeat is less annoying)
- No more floating razorgrain (https://www.nexusmods.com/fallout4/mods/13823)
(not really essential; but my OCD kicks in everytime I see them floating)

Quality of Life:
- Faster Terminal Displays (https://www.nexusmods.com/fallout4/mods/937)
- Power Armor Fast Exit and Enter (https://www.nexusmods.com/fallout4/mods/586)
- Simple Wait Anywhere (Lightweight) (https://www.nexusmods.com/fallout4/mods/55597)
- Sofa Surfer - Sleeping on Couches (https://www.nexusmods.com/fallout4/mods/24944)

It's cheating; but if you have enough of the lockpicking and hacking-minigames
- Easy Lockpicking and Hacking (https://www.nexusmods.com/fallout4/mods/31527)

Audio
- Project Reality Footsteps FO4 (https://www.nexusmods.com/fallout4/mods/35904)
- Reverb and Ambiance Overhaul (https://www.nexusmods.com/fallout4/mods/10189)

Settlement
- Place Everywhere (https://www.nexusmods.com/fallout4/mods/9424)
- Faster Workshop (Workshop Lag Fix) (https://www.nexusmods.com/fallout4/mods/35382)
- Longer Power Lines (https://www.nexusmods.com/fallout4/mods/2241)
- Settlement Attack Spawns Outside the Settlement (https://www.nexusmods.com/fallout4/mods/57685)
- Settlement Repair Bot (https://www.nexusmods.com/fallout4/mods/37933)

You should be carefull with "Scrap Everything". You can literally scrap everything (even roads etc.).
In some cases it can cause serious issues with pre-combines. If you just want a cleaner settlement use
- Clean My Settlement REDUX (https://www.nexusmods.com/fallout4/mods/58757)

HUD
- FallUI - HUD (https://www.nexusmods.com/fallout4/mods/51813)
- FallUI - Inventory (https://www.nexusmods.com/fallout4/mods/48758)
- FallUI - Icon Library (https://www.nexusmods.com/fallout4/mods/60579)
- FallUI - Map (https://www.nexusmods.com/fallout4/mods/49920)
- FallUI - Workbench (https://www.nexusmods.com/fallout4/mods/49300)
- FIS - The NEW FallUI Item Sorter (https://www.nexusmods.com/fallout4/mods/60580)

If you have a Ultrawide-Monitor
- Ultra Wide Interface (21x9) (https://www.nexusmods.com/fallout4/mods/65677)

These mods should be safe to use and a good base to add mods on top of it.

Great Mods, but they overhaul the gameplay (I don't know how far you want to mod your game)
- REAL.AI (https://www.nexusmods.com/fallout4/mods/72923)
- Sim Settlements 2 (https://www.nexusmods.com/fallout4/mods/47976)
- Everyone's Best Friend (https://www.nexusmods.com/fallout4/mods/13459)
- Better Locational Damage (https://www.nexusmods.com/fallout4/mods/3815)
- Better Explosives (https://www.nexusmods.com/fallout4/mods/3648)
- Better Power Armor - Redux (https://www.nexusmods.com/fallout4/mods/61146)
- Better Companions (https://www.nexusmods.com/fallout4/mods/18547)
- We Are The Minutemen (https://www.nexusmods.com/fallout4/mods/6443)

If you play in Survival Mode
- Unlimited Survival Mode - F4SE (https://www.nexusmods.com/fallout4/mods/26163)

Update:

Suggestion for Fallout 4 safe-modding:
- Don't mess with pre-combines!
(leads to FPS-Drops, flickering and sometimes whole buildings can disapear and npcss/you can fall through the floor)
- Don't remove script-heavy mods/overhauls mid playthrough!
- Use a Mod Manager! Vortex is fine for beginners and it has a "build in auto-mod-sorting-feature".
- Take a minute and read the descriptions (for conflicts with other mods and as an excuse to drink more coffee).
- Look out for Compatibility-Patches (in case of known conflicts).
- Use LOOT in addition to your Mod Manager (LOOT have more usefull tips like if a mod needs addtional cleanning)
- Use FO4Edit (for cleaning/editing mods and to create a "Merge-Patch")
- Use Wrye Bash (to create a BASHED-Patch for leveled list)

Tools for Fallout 4
- LOOT (https://loot.github.io/)
- Fallout 4 Configuration Tool (https://www.nexusmods.com/fallout4/mods/102)
- FO4Edit (https://www.nexusmods.com/fallout4/mods/2737/)
- Wrye Bash (https://www.nexusmods.com/fallout4/mods/20032)
- Optional: FallrimTools - Script cleaning and more (https://www.nexusmods.com/fallout4/mods/22633)

Video-Tutorials
How to Clean Mods & DLC
https://www.youtube.com/watch?v=YpRinGULJGw

The BEST way to create a MERGE PATCH
https://www.youtube.com/watch?v=x0kEWbGnYik

How to use FallRim Tools (Optional for "cleaner" save-files after removing mods)
https://www.youtube.com/watch?v=hyPDQuWg6jQ

thanks guys

I'm just doing some research before I decide whether or not to buy Fallout 4, and mods obviously is a part of this as these Bethesda RPGs basically need community fixes.

Anyway, a couple of questions I have:

I read that there's an issue where the player falls through the floor in certain locations (I saw Museum of Freedom and Cambridge Police Station) as well as a crash to desktop issue during the Hunter/Hunted quest. I also saw that Bethesda have said the falling through the floor issue is caused by modified ini files. So, do any mods fix these issues?

What order should essential mods be installed, considering that I don't want to use a mod organizer and will instead install mods manually? How can load order be changed for mods that use ESP and ESL files (preferably without using additional tools to install)? From igooseman's post above, I'd probably be looking at the bugfixes and essential mods, and the must have mods.

I also saw a Canary Save File Monitor mod on Nexus. Is this useful and recommended?

EDIT: Oh, and I saw some posts on the Nexus mod page for the Unofficial Fallout 4 Patch saying that it breaks some of the NPC outfits so that loads wear the same clothes. Is this the case for most users and can it be fixed? Or am I better off waiting for a new version, or even just not using the Unofficial Fallout 4 Patch, or is it really that essential?

That's really good to know! The last time I played everything had to be locked to 30fps or 60fps via your graphics card settings. For your load order I'd use something called LOOT (Load Order Optimizer Tool) which will give you the best order 90% of the time and I personally use Nexus Mod Manager Community Edition, because the interface is far less bloated than Vortex and doesn't require reading through a manual to setup. Not sure if it's been updated since 1.0. NMM also lets you modify the load order. I know from experience it breaks mods, which is why I only recommended it for a vanilla playthrough, but now I know it breaks vanilla content I'd say don't use it at all.

Anyone bummed out about Creation Club, well if you already have the Steam version, you can use MO2 and package them up as mods. Works great.
Or (and I haven't tried yet but) transfer over from the Steam version.

I feel bad for the people who bought stuff on Creation Club

I updated my mod list post and like I wrote my list is "safe to use". My personal modlist is much larger and I had no issues after 1000+ hours.

There are some popular mods everyone uses; but these mods can break the game/even corrupt your savefiles in the long run. I would say mods like Amorsmith Extended, Scrap Everything, Boston FPS-Fix, most of the "Cleaning-Mods" etc. are not safe/have too much conflicts/are not up-to-date anymore.

I'm curious to see how far they take the Creation Club in Starfield.

I used Vortex and MO2. In his case Vortex should be "easierer".

Maybe Bethesda will push modders more to the Creation Club and try to monitize mods. They have tried it before. But I don't want to accuse Bethesda in advance or give them ideas.

It's ok, I don't feel bad about what you do.

igooseman, thank you for that mod list.

I wanted to play Survival mode but I also wanted to change the timescale, because the vanilla value of 20 is just way too fast for my tastes.

I tried using timescale mods but none worked. I downloaded the "unlimited survival" mod you suggested and, now that I can use the console, I can change the timescale myself.

Well... have fun! ;-)