I own the regular version on Steam and I had to try installing different patches to get past the tutorial, otherwise the game would crash at the exact same spot every time. Will I have to do the same here?

I'm 5 hours in without installing any patches. Just reached the GNR Plaza. No crashes.

GOG version is outdated now. Better or worse - cant say for sure. I hear latest update somehow changed sys.reqs and bring bugs. Im myself never faced compeltely unplayable single-player games on Steam\GOG\etc.

Try to verify game files in Steam Library - tiwce in a row. Remove game user folder (documents or appdata or whre it stored?), relaucnh and reconfigure game and start compeltely new playthrough.

There can be ore useful info (first of this Wiki for games Steam versions)
[url=http://www.pcgamingwiki.com/wiki/Series:Fallout]http://www.pcgamingwiki.com/wiki/Series:Fallout[/url]
or not useful and wrong. This is Wiki - check it and try tweaks from there at your risk.

I can't get it to launch. I keep getting a crash to desktop right after selecting "Play" in the launcher. Been looking for a fix all day.

GOG version is stable - 100%. Offline one.

You may want to check out this post and see if it helps maybe.

https://www.gog.com/forum/fallout_series/fallout_3_wont_launch_after_hitting_play/post2

A lot of times, reseting the ini or conf file can fix things, since it involves initial settings for the game.
.

On Steam-version - you'll need/want to do the 4GB Patch; get rid of that G4WL junk with XLiveLess or something of that sort; downgrade to older FO3 version (to get back to version 1.7.0.3); grab FOSE (since that works w/ 1.7.0.3) - and that's just to get it going.

Can't speak for GOG-version - but according to PC Gaming Wiki, GOG version comes w/ 4GB RAM Patch, mulit-core fix, and No G4WL...so that should stop a few steps in the actual process to mod it up properly.

Starting steam.exe as admin also can fix some issues with steam client itself and for many games.

GOG Version just works fine on my system...vanilla or modded :)
Don't know, what others doing with their systems...drivers outdated, stupid system tweaks ?
Same goes for Fallout: New Vegas....vanilla or modded, it just works fine.
I try to understand, when someone complains about the game, but mostly the informations just rare to get any ideas of it.

Operating System
Windows 10 Pro 64-bit
CPU
AMD Ryzen 5 3600 60 °C
Matisse 7nm Technology
RAM
32,0GB Dual-Channel Unknown @ 1066MHz (15-15-15-36)
Motherboard
Micro-Star International Co. Ltd. MEG X570 UNIFY (MS-7C35) (AM4) 31 °C
Graphics
PLG2788H (1920x1080@144Hz)
NVIDIA GeForce GTX 1060 6GB (ASUStek Computer Inc) 29 °C
Storage
465GB Samsung SSD 860 EVO 500GB (SATA (SSD)) 27 °C
3726GB Western Digital WDC WD40EZRX-00SPEB0 (SATA ) 34 °C
931GB Samsung SSD 970 EVO Plus 1TB (Unknown (SSD))
Optical Drives
TSSTcorp CDDVDW SH-224FB
Audio
Realtek High Definition Audio

/edit as gog2002x mentioned above: try to delete the Fallout_default.ini file and start the game again, this seem to work often ! ;)