Yes, buy and play Fallout, Fallout 2 and Tactics. You can get all three pretty cheap
I would hope that whatever is chosen that the size of the area to explore is much larger than those before it.
Fallout and Fallout 2 aren't about exploration just like how New Vegas isn't about exploration. Doesn't mean there isn't places to explore. If you haven't played New Vegas, play that as well. The game worlds of the orginals aren't as big as the new games bu they are awesome none-the-less.
I don't think anyone wants the game to end
Not sure what you mean by this. Fallout, Fallout 2, Fallout Tactics and Fallout New Vegas all have multiple endings based on how you play the game. I very much want all Fallout games to have an ending. Even Fallout 3 had an ending, it was total crap but it was an ending.
From the sounds of it, Fallout 3 is the only Fallout you have played. Not bashing you, but the sooner you play New Vegas or the orginals the better.