Depends on what you're into.
IMHO - Fallout is one of the best RPG series out there period.
Fallout 1 + 2 are great, if you're into very old-school CRPG's with turn-based combat. They're both classics, IMHO. With lots of decision-making; off-the-wall humor; plenty of blood + guts; foul language; and a different post-apoc' setting for a RPG - definitely ground-breaking, when they both came out.
Fallout 3 + Fallout: New Vegas all have meaty DLC's. So, those are games you should go Complete on.
So, for
Fallout 3 - you're best going w/ GOTY Edition - which comes w/ all 5 DLC's. Point Lookout + The Pitt really stand-out, if you ask me.
For Fallout: New Vegas, you want the Ultimate Edition. Old World Blues is one of the best DLC's that I've ever played - period.
Also, to run
Lead Designer Josh E. Sawyer's HardCore Mode, you actually do need base game + every single DLC - so, if you want to use that, you do need Ultimate Edition.
As for
Fallout 3 GOTY + New Vegas, they're always going to be a debate of what's better. Both are a great, in their own ways.
First up,
Fallout 3. IMHO - not many can top Bethesda when making huge game-worlds to explore and get lost in than Bethesda - and a destroyed East Coast back when it came out looked incredible. Fallout 3 was certain fresh as can be, back when it came out. Fallout 3 set the standard of how a modern-day Fallout game could be made for the modern-era - with its allowed 1st person/3rd person view-switching on the fly; real-time combat; and the VATS system (you build-up action points and then can jump into a turn-based style mode like Fallout 1+2 and watch the violence play-out in a cinematic manner. Fallout 3 is often a lot more serious than what New Vegas has going on; and the writing here is certainly not in Obsidian's league; but it's still one of Bethesda's best, actually.
New Vegas is from Obsidian - many of the former FO2 designers such as Chris Avellone + Josh E. Sawyer were involved in that. Obsidian are experts w/ character, storytelling, narrative, prose, and especially tons of decision-making - especially w/ having Avellone on board; dude's a RPG legend (i.e. Fallout 2; Planescape: Torment). So, while Fallout 3 might've been fresher b/c how it completely modernized the FO formula - New Vegas brings back the often twisted and tongue-in-cheek humor; and the personality that was often found in the earlier Fallout games (Fallout 1 + 2). Also, there's a lot more decision-making and emphasis on your stats can cause more and different options available; especially when compared to FO3.
But, still - all of the FO games are great, IMHO. You can't go wrong w/ any of those, IMHO.