So yesterday I finished Fallout 1 and I'm eager to jump into Fallout 2. But before I do so I am aware that there are many patches and mods for this game. Before I begin this game is there any mods or patches that can be recommended to me to install so that I may have the best play experience possible?

You should take a look at this thread.
I can't recommend any mods from personnal experience cause i'm in the same situation: Finished Fallout and getting ready to start Fallout 2 :)

Prator, I really like that idea. Actually it makes the most sense to me too. Just enjoy the game for what it was first.

I played Fallout 1 Vanilla and beat it, and am playing 2 Vanilla. I would suggest Vanilla is the way to go for an hour before diving into the lake of mods.

Beat Fallout 2 vanilla, despite all it's cut content, it's still fun. Once you are done, try the restoration pack since it helps make the game more fleshed out.

I started it with the Killap's restoration patch my first time. Personally, if it restores cut content, I think it's a good bet to start with. The other view is that you can play it vanilla to get the "theatrical" release, and then again for the "directors cut" version.
You'll probably get more than one playthrough from it so I'd personally recommend vanilla for the first taste.