The real order
Fallout 1 — No doubt the best in class for story. I don't think any of them even come close. This is really the sole reason I rank it #1. Also set the tone for the series' setting and atmosphere. At the same time, it was also far more serious than any of the others, though New Vegas did strike a pretty good balance here too. To top it off, there was just as much choice and consequence and world reactivity as any other product in the series. Introduced us to S.P.E.C.I.A.L., oh and how all those stats actually affected your playthrough (F3 I am looking at you). Some people complain about the combat, but I came to love it. Finally, who could forget that ending? Especially if you played the low karma do-what-you-got-to-do wastelander that I did my first time through. Fallout is my favorite series, and this is still the game I have played through the most.
Fallout 2 - Gameplay-wise it is the same as the first with some particularly notable improvements with companion interaction. The story and world is bigger, but also less thematically consistent than in the original. Still great choice and consequence, become a mobster, a porn star, a jet junkie, get forced into marriage at gunpoint — so many great little things about this game. If you like how the originals played, this is the easiest to go to back because of the slight improvements, the higher level cap, and of course because it is the one all the mods come out for…just talking about the first two there.
Fallout New Vegas - Finally a true successor to the original Fallouts. I actually quite enjoyed the western vibe, the characters were varied and interesting. In some ways, the C&C in New Vegas was more advanced than in the original games. You could affect the ultimate outcome of the world to a far greater level than in any of the other games, even take a neutral or libertarian sort of approach where you choose no sides. It brought the series back to its roots in a couple other important ways too. Character development had greater impact on your playthrough than in F3 and the level scaling appeared to be completely removed. Explore all you want, but do so cautiously! I am not going to lie, I loved this iteration, though there are probably a couple elements that could have been done to make it feel more like the originals. I really hope Obsidian gets another crack at the license.
Fallout 3 - I am not going to bash on it, though I sort of feel like I want to. The world is completely different, but it is still interesting and unique, and a lot of the great atmosphere from the originals translated well. S.P.E.C.I.A.L. feels incredibly watered down. C&C is there, but likewise feels a tad watered down. Bethesda made a great world to explore, though the level scaling was a definite deviation. Fun game, but also the only one that never sucked me in all the way. Also the only one I still have never finished (I have never actually finished a single Bethesda game). I have had fun cruising around the wastes as a booze and jet-addicted wastoid, and hopefully some day my character will summon the courage to finish his quest and save the world.