An LP is tempting to play lead to my Dot's rhythm, but I'd probably go for a Tele (with humbucker bridge that can be split for single coil sounds, or maybe a P90) or a firebird to get the mini hubuckers.
My next guitar is going to be a lifetime keeper Fender Strat.
My favorite guitars will always be Les Pauls and Strats, with a few others tossed in like McCarties and various G&L's. I want a strat that I'm going to be 100% happy with. Even though I don't like the idea of signature models, the Eric Johnson strat in alder sunburst/maple is looking like a top contender. Otherwise, I want a CS NOS strat that's been refretted with medium jumbos.