Before you ask I do have the Steam version do to getting the full bundle of all the games but I want to get the GOG versions since I'm have been having major problems with console commands locking out achievements, out of memory to rapid fire crashes to the point the mods I installed didn't work or I didn't do it right and I gave up and uninstalled everything.

Will I have the same problems here on the DRM free version or is there a full list I need to get the game running? Because I really want to play New Vegas but it's impossible right now.

Here are my PC specs:

Processor AMD Ryzen 9 5900X 12-Core Processor 3.70 GHz
Installed RAM 32.0 GB
OS Windows 10 Pro
GPU Nvidia RTX 3070 Ti

I've played Fo:NV without mods (Steam version; it was Christmas gift while it was new game) and with mods with GOG.com's version. There is a very helpful website with great guide for modding Fo:NV:
https://vivanewvegas.moddinglinked.com/intro.html

It worked for me and thanks to that guide I was able to play entire game without any errors nor crashes.

If somebody is interested there is guide for Fallout 4 as well:
https://themidnightride.moddinglinked.com/intro.html
... but it didn't worked for me (with GOG.com's version of Fo4 game). Maybe I did something wrong but Fallout 4 is not a game I want to replay so I skipped modding Fo4 game.

I had to dig through my archive of downloaded FNV mods to see just what I used to resolve this issue, back when I bought FNV on GOG in 2017.

Nexus Mods - Using the console doesn't disable achievements
This is a plugin for the New Vegas Script Extender

A lot of folks now days very forcibly "recommend" you use JIP LN. I've no experience with it, so I can't comment on if it works properly with FNV on GOG.
What I do know, from first hand use is, NVSE and the plugin mod I linked to does work on the GOG release of FNV. In my playing over the years, I've got 59 Achievements on GOG. There's still more I need to earn.

Ok I'll look into it.