I also have a LP faded and love it. It's a little "rough" in that it lacks binding, the Gibson logo is painted on the headstock, and you can feel the woodgrain on the back of the neck and the fingerboard.

In your price range, you won't have to worry about this and you should have some choices.

From when I was researching Les Pauls, here is what you need to figure out because you have some choices:
- Do you want a 60's or 50's style neck (60's is slim taper, 50's is fatter).
- Do you want humbuckers or not?
- Do you want to be able to switch the pickups between single coil and humbuckers? Just know that switching them to single pole mode doesn't magically make it sound like a strat.
- Do you care about the fingerboard wood? At least for the Studio line, this year they changed to a different fingerboard wood. If you care, you may want to find a used guitar with a rosewood fingerboard.

Unless you have experience with these parameters, you'll have to spend some time comparing them in the store.