Fallout 2, i was not crazy about the humor, i actually like 1 and 3s approach to the the wasteland, like you know, it was a bad thing, but fallout 2 had so much you could do and had interesting writing i actually cared what people said and would search the wasteland for just a bit more info, fallout 1 was fun but a bit short, fallout 3 was the most fun to play, but the writing and story was uninteresting.
And fallout 2 had so many options, first of all theres stupid, which is surprisingly fun but more importantly you where free to play like you wanted, i tried playing HtH in fallout 3, bloody hard, even on super easy it was way harder than it was in 1 and 2.
Edit: As of writing I'm the only one who didn't pick fallout 3, i played the originals for the first time in 09, and i really didn't see any problem with the graphics, if your not playing 1 and 2 because your afraid they will be impossible to be immersed in because of the rather dated graphics, I'm here to tell you "worry no more", honestly they are just to much fun to play and to interesting for you to even notice the graphics, i don't say you shouldn't pick fallout 3, all I'm saying is you should play 1 and 2 as well, also they will help you enjoy new vegas even more (i suspect that knowing who NCR is will help you allot), and if for nothing else you can find out what jet is (it will blow your mind).