If you're interested in the entire IP, ALL of Fallout, rather than just the past few years, Fallout 1 & 2 are very cheap, have good stories. The gameplay is... not slow, but rather deliberate. Not for everybody. There are tons of Lets' Plays out there on the two games, so look some up if you wanna see gameplay.
If the gameplay of those two don't look appealing, don't play them. Simple as that, you won't enjoy it. And even better, you don't need to know the plot of the first two. You don't. The series is a bit like Far Cry, in the fact that they could all exist in the same universe, but no person you play has an impact on any other game in the series.
So yeah, if those don't look appealing, try Fallout 3. Its one of the best value-for-dollar games out there, its really fun, and the DLCs are worth getting. In fact you may not even want to get a patch for a while, as there are quite a few glitches that people like to use that were fixed in the patch (see Mister Sandman glitch).
But yeah, definitely Fallout 3, no matter what. If you're interested in the IP as a whole, go check out the first or second one. Don't go for the non-numbered entries in the series, like "Brotherhood of Steel". Just trust me on that, unless you become obsessed with the franchise. I haven't played New Vegas yet, so I can't give an opinion on that.
Lost In The Void said:
FO3's story is shit and the characters unbelievable.
Playing Fallout solely for the characters and story is like watching The Godfather for the special effects. Any installment in the series. The game's main plot can keep a dark tone, but it never takes itself to seriously. For every scene of a father martyring himself for his child there's a Republic of Dave, which I think is an important, and successful, design choice made for FO3.