Hi, just bought Fallout 1. I've seen a bunch of different patches out there and was wondering are any of them needed? Also are any of the bugs caused by the patches game breaking?

Thanks.

No patches are required, all official patches are already in place.
Bugs caused by patches? Shouldn't be any.

Fan patches do fix a few minor quirks and offer enhancements.
For a more detailed reply, see here.

There is something to be said for installing, at minimum, a patch to bring Fallout 1 in line with the US version. The European version, the last to get official updates and therefore the version GOG uses, has edited out the visible presence of children. Fallout 2 doesn't have this problem, as the goal wasn't to censor but to provide the best product in both cases.
So you may wish to decensor your Fallout 1 install. Otherwise, and this is as per the original European release, things may get a bit odd.

Would installing any of the patches make the game more enjoyable?

Install the patch which removes the censorship. I don't recommend installing more.

Yes. The patch which makes the children visible again makes the game more enjoyable as you won't randomly and arbitrarily suffer the Childkiller reputation for tearing about with automatic weapons (including assault rifles) and accidentally tagging ghostly, invisible kids.
Not that there are many kids, but it's still not the sort of thing you want to encounter accidentally. This is the aforementioned decensorship patch.

Past that? If you find the NPCs to be unpleasant in their implimentation (which I did not, but some have), there's the TeamX NPC Mod. Nimrod has a few dialogue fixes, grammar and such.

The NPC mod allows you to change npc distance to you, I believe.
It's annoying when you have to load a previous save or kill the npc because he/she is blocking your path.