Coming from a neutral perspective as much as possible:
Fallout 3: Unique story set in DC wastes. Only utilizes names from previous titles in the series.
Operation Anchorage - Unlocks unique weapons. Influences standing with the Outcasts. Play at any time
The Pitt - No story influence. Introduces several new melee weapons, guns, and some clothing. Play at any time.
Mothership Zeta - Unlock unique items. Changes alien rifle from god powered (limited ammo) to balanced weapon. No story line influence. Play at any time.
Point Lookout - Introduces several quests and items. No story line implications. Play at any time.
Broken Steel - You should play this. It expands maximum level, and allows powered armor equip. Continues story post original ending (no spoilers).
Fallout NV: Continues the story along the lines of 1 and 2. Utilizes same gameplay, engine, and mechanics (with relatively minor changes) as Fallout 3. Brings back character skill selection methodology from 1 and 2.
DLC still coming, and I couldn't be bothered to play after the first half hearted release.
If you're just starting, go with NV. It is, to my opinion, a better match to previous story lines. The game engine, graphics, and structure was kept between the two games, so actual gameplay is very similar (though someone is going to bitch me out for saying this, due to the small differences) in both games. After 90+ hours of one game you'll likely be burnt out to the other.
Once you've gotten a taste for the game, check out the Nexus. They have tons of user created mods to do just about anything. I've currently got all of the unique NV weapons in 3, and well over a dozen extra fun missions. This fails to mention the enormous stability improvements, and fixes, that the publisher wasn't competent enough to release. Seriously thous, check out the Nexus for either 3 or NV. It will drastically extend the life of the game.