Fallout 1 is my favorite, maybe for partly nostalgic reasons, but the plot, atmosphere, music, writing, humor... it is complete. I'll always remember seeing the opening movie the first time. I get that a lot of gamers would be turned off by the subpar graphics. And the inventory system does kind of suck.. That said, it's such a durable game. You can do anything.
Fallout New Vegas is splendid, it's my go-to game for a Fallout fix. The story is cool (and flexible), there are great characters, kick-ass equipment, the "western" feel.. It's almost perfect except for the stoooopid bugs that still happen --- the game will freeze, hang during loading, sometimes crash --- after awhile I can't overlook that. I always come back, though. FNV is a must-play.
Fallout 2 is flat out awesome, improves on 1 in many ways, except it is lighter on the atmosphere, and it winks at the fourth wall too much. Bigger game world and better inventory system. It's more of what made 1 great.
Fallout Tactics, is an underrated game. I know a lot of the die-hards hate it, but I always found Tactics to be a helluva lot of fun. You have to go in knowing it's a squad-based tactical game, with a fairly linear story, and within that you build whatever character & team the game allows. Of all the early Fallout games, the graphics/sound of Tactics still hold up.
Fallout 3 is a fun sandbox to run around in, although the story is ridiculous and some of the areas (Little Lamplight...) are so bad it almost kills the game entirely. (My opinion.) What it has is a good world, and if you play on PC and have access to mods you can have a blast just banging around the capital wasteland. It's more stable than FNV, and that matters when you wanna run around for a couple hours.
I've started Fallout 4 recently, and can't rate it yet. So far... the world is interesting & there's a ton to do.