Howdy,
I've been playing about 17 years now. I'm a lead man. But I know what nice rhythm sound your looking for. I have an esp ltd. It is a fixed bridge guitar and I have 10's on it for my "full" sound. On the other side of the coin, I have an esp with a Floyd rose and 9's for when I want to shred. I happen to love esp. No real reason, just a preference. You can get a nice les Paul knockoff that will play great and produce the sound your looking for pretty inexpensively. A nice set of heavier strings and your golden. And a fixed bridge guitar will always stay in better tune than a guitar with a floating bridge. Always. Unless you have serious action/warping problems.

look into an epiphone. Your still a relatively new guitar player and its a really nice intermediate guitar.