Yeah, I don't even think I'd heard of Fallout before playing 3. There are only two minor things I can think of that make significant references to the prior games. If you want, you can go look them up on the Fallout wiki, I enjoy reading the articles there. They go into more detail about the alternate-future nature of the setting and can answer just about any questions you may have regarding the lore.
Only thing is, Fallout 3 seems to be particularly buggy on PC, especially on Windows 7. It freezes up constantly, I haven't found a fix yet. If you can, pick it up on 360 or PS3.
I was considering picking up the New Vegas Ultimate Edition on Steam, but not if it's as bug-addled as FO3 GOTY is.