I'd still recommend Fallout 1 (patched), Fallout 2, 3 and New Vegas.
If you're more of a recent gamer, then you might want to try New Vegas out first. It pretty much sticks to modern RPG conventions, which means a lot of hybrid shooter gameplay. If you're not at ease with having to crunch numbers or having to wait turns, it's a good starting point. It's also an improvement over Fallout 3 in several small, but not exactly negligible areas. Weapons can be modded, the game has an iron-sights mechanic, companions are better handled overall...
On the other hand, if you've got the stones for a more classic experience, try Fallout 2 first. It improves the second one by removing the egregious time limit the first one had and essentially plays out like a turn-based isometric sandbox.
And obviously, if you're *really* jonesing to get the full chronology firsthand, then find Fallout 1, patch it or mod it so the time limit's removed, and go from there.
The third game sits nicely in the middle, seeing as it's the series' introduction to Bethesda's usual mechanics. If you're familiar with the Elder Scrolls series and particularly with Oblivion, then you just might want to start out with Fallout 3.