Count me in as ready to lose about a few hundred hours of my life playing this game. I was oblivious to the Fallout series prior to Fallout 3. On a whim, I decided to give it a shot. I was hooked instantly.
Fallout New Vegas isn't a sequel but another story within the same world of Fallout. Not much info released yet on the game (although there are some rumors that are very likely). More info on the game will come in the next couple weeks via Playstation and Xbox's magazine.
My understanding is that all the characters are in the game whether you do the Amiibo thing or not. BUT if you get the Amiibos, you can level up your character, take it to play on your friends' systems, etc.