i personally wouldn't even be worried about it...

get a guitar that feels good and plays nice to you... Billy's tone doesn't come from his guitar since most of the time he's using plain-jane models like a Les Paul Special... which has only one humbucker in the bridge. The amp really isn't going to cause much of a problem either... Just get an amp that will project the sound... You can always get a cheap effects processor to get what tones you want... Most of the people that are going to listen to you music (if you're playing Green Day) aren't going to be too concerned with how your amp and guitar sound in comparison to Billy Joe Armstrongs... Don't sweat it... Just do what feels good to you. That's part of the punk philosophy anyway... Don't do something based on something someone else is doing. Make the music your own... If that means you have slightly different tone... then so-be-it.