Well, if you're gonna go Green Day
I believe 'American Idiot' was supposedly a primarily P-90 sound, so that would probably be a good place to start. The Epi Jr is probably about the equivalent of a Squire in terms of build quality (unless your Squier is an 'Affinity', which are decidedly more cheaply made). That being said, if you can find one of the Juniors with a P-90, I think you might like it. It just seems like a very punk guitar, as well as a rocker. Just my opinion.
If your use to a strat-type, an LP-type (not LP Jr.) is going to be considerably heavier, so you may or may not like that feel.
I always suggest you go and play some different guitars UNPLUGGED first to find one that feels good. You'll know it when you find it. Maybe it'll be too much money, so then you'll have to set about finding one that feels 'good enough'. THEN worry about how it sounds. You can do a lot with swapping out pickups, pedals, amps, modelers, etc. to modify the sound. What you can't do is make a guitar feel good that doesn't.
I can tell you to avoid being swayed by what the bands you like play, but it won't do any good. You won't really listen anymore than I did, or do now. If Hendrix was playing a Strat, and Clapton had an SG, I sure as hell didn't want some old Gretsch. Bleh!
It's funny, a younger guy I know says when he plays a Les Paul, he feels like he's playing an antique. He hates 'em. But he's from the PRS generation, so don't listen to us, go pick out what you like. And bang out something new and different and bring it back here and play it for us.
Have fun.