In my recent playthrough of Fallout New Vegas, I tried to load my save file but I got stuck in a loading screen for way too long that I had to shut down the game.

Apparently this is a common bug for New Vegas that has yet to be fixed.

Any mods and Fan Patches that is important for this game?

Don't know which one do I get.

Please put in into the games forum not here.

Those forums take forever for a response. There's more user activity here.

I mean clearly you responded to me faster by telling me to go there.

I played New Vegas recently (in November/December), and I used the wiki guides from the Fallout New Vegas subreddit: Premodding Guide (stuff that's necessary to check before installing any mods) and Modding Guide (recommended mods). The tl;dr version is that you'll certainly want to install everything in this section, with most notable for me being the 4gb patcher, nvac (New Vegas Anti Crash) and New Vegas Tick Fix.

Also with the loading game bug loading screen you can click on NEW GAME then after the new games starts you can load your save properly it works.

Last time I played the main bugfix patch for NV was Mission Mojave.

If you use Yukichigai or YUP, keep in mind that it also has started "fixing" mechanics they feel aren't balanced or weren't intended to work the way they do in game. If you're cool with that, it's updated the most frequently, if not, there are other mods out there, like Mission Mojave, etc.

Mission Mojave is heavenly outdated and hasn't been actively touched since 2015 (the devs themselves called it the "finalised" version).

Better go with Yukichigai Unofficial Patch + Unofficial Patch NVSE Until GOG changes the forum that won't happen.

EDIT: I totally forgot; I meant NVSE not Plus. Been a awhile ;)

But do those unofficial patches include the fixes from MM?

That, I'm not sure about, and since it's been taken over and updated by other people, as has happened a lot lately with older mods that haven't been updated for years, I can't 100% recommend it unless you're entirely cool with said updaters' ideas of what the mechanics should be, as opposed to simply fixing bugs, errors and leaving things like mechanics and content the eff alone. I don't use it at all, I use MM and thus far, it's been fine.

That said, I don't run a huge mod load.

My list right now consists of:

UIO
JIP LN
NVSE
Roberts Body Replacer for better NPCs
Type 4 Body replacer for better female NPCs
Ojo Bueno
MG's Neat Clutter pack
MTUI
Interior Lighting Overhaul
NV Interiors
Book of Water
Book of Steel
Book of Flesh
NV Bounties I-III
Wasteland Flora Overhaul
Ground cover Overhaul
Spice of Life (I really enjoy this, as it adds things like dufflebags, rucksacks, and a large variety of lore friendly clothes and armors.)
WRP
WMIM
Megaton Hairs
Distributed Necklaces and chains
Impact

You could probably get away with eliminating things like the replacers and a few other things from this list, tbf, if you're just looking for bug fixes and nothing that changes the visuals.

If not a direct copy-paste of code, I would imagine they fix much the same from what I've read (mod reqs by others), however, since I'm pretty late in the NV modding arena I personally haven't done any direct comparison/testing or read through the whole list. I just skipped MM all together and don't think I will try it in the near future.

YUP: Because, unlike MM, those two in combo is considered for "purists" that focuses on bugfixes (the latter needs scriptextender to fix things beyond what YUP can on the "swiss-cheesed" engine). Also, MM changes so much it can become a problem for other mods (although, some cross-fixes is offered but still not ideal).

EDIT: If you want to take a look at the list without dl it: https://pastebin.com/JjzYSGuX

Lol why is OP's post downvoted?

I'm guessing because OP decided to skip the Fallout subforum entirely, in spite of obviously being aware of said subforum, and uses "I'll get an answer faster" as an excuse (which is about on par with the self-fulfilling "The subforum is a graveyard" excuse). The fact that the answers are already in the subforum, or that this thread, like so many others, will just disappear in a week or so, and therefore not help anyone else with the same question, doesn't matter. All that matters is getting an answer quickly, without any effort.

Granted, gog doesn't make it any easier by not giving proper links to the subforum, or providing a way to limit the subforum list to games you own.

Also granted, if this post had appeared in the Fallout subforum, I would've ignored it entirely, rather than checking to see if anybody at least chastised the user for not using the subforum.

Yeah, I'll be honest, half the time, I forget the subforums still exist.