I voted Fallout 2 because, while 1 is the more concise and finished classic, 2 is the big crazy ambitious mess of a follow up that you could lose yourself in for a year, and I did (shades of RDR2). Forget just doing post-apocalyptic Fallout stuff; I worked for the mob, became a porn star, and eventually POTUS (well, I had his ID badge, anyway =). Fallout 2 isn't just the best Fallout game I've ever played, I could make a case it's the best game I've ever played, period. Having said that, unfortunately for those that really didn't get into it or Fallout 1 at the time, I don't know how accessible it is anymore. Like I certainly am not going to replay it today, and I just threw it into the GOAT (G.E.C.K.? =) conversation.
As for the Bethesdas, I don't really count those among the first two Fallout games. They're something else, like a remake or spinoff, even New Vegas though it's a nice compromise and basically the the closest thing we could get to fulfilling the original vision of Fallout 3 by the Black Isle team (I'll always be grateful to Bethesda for letting this game happen). So, I'm not bashing them either, because playing Fallout 2 I dreamed of doing it in first person and at least got somewhere close between 3 and NV. Fallout 3 is a pretty good semi-early example of an effective big budget soft reboot/requel too (before it became the norm in film as well as games). It basically recycles and reworks the major plot points and story beats of Fallout 1 and 2 into a more visually immersive and streamlined package. But it was more smoke and mirrors than the meticulously handcrafted, interactive worlds of the originals. NV brought that craftsmanship back the best it could, but was still limited within Bethesda's framework, then Fallout 4 doubled down on the cinematic experience and combat, which was fun, but that much more dumbed down when it came to immersion through consequential interactivity. At least relative to the originals, I mean I don't hold every or maybe ANY other game to these standards ("You mean I have to follow the story progression? That's like a baby's toy!"), but if it's called Fallout I do because that's what made those original games special.
1. Fallout 2
2. Fallout
3. Fallout: New Vegas
4. Fallout 3
5. Fallout 4
0. The rest