Sounds good.
Let's wait until we jump into the game, and see how our characters feel once we get there. Good thinking on Spidey, and in a way he does just that... or wants to, up until uncle Ben gets killed... so yeah, you're feeling the character just fine.
Any team would be Fantastic, even if they're not the FF. Don't worry about being powerful enough, though, the game is more story-focused. It can genuinely handle Hawkeye and Cap teaming up with the Hulk and Thor, and having the same chance of success... depending on what they're doing (hawkeye's aim should be as good as Hulk's punches).
The Basic game has Breakout as an initial event, where the new Avengers assemble to include Spidey and Wolverine. Really, after reading Wolverine vs. Marvel Universe (surprisingly good story, unfortunate title), I get the feeling that everyone knows everyone, but they have teams that live together.
EDIT: not that we're doing Breakout! if you get the game, you can run that for your home group.