Guitars with tilt back headstocks can be prone to a neck break from a fall or impact to the headstock. I wouldn't let that discourage you from choosing a set neck, tilt headstock guitar, though. It happens, but the repair is straightforward and doesn't usually cost a lot to fix.

Epiphone makes a good, solid guitar. Yes, many of their models are imported copies of Gibson designs, but the guitars out nowadays are of excellent quality overall. You may have to play a couple to find what you like, but that goes for every guitar maker out there that mass produces their products. Squier does the same for Fender (overseas made copies of Fender designs), and some of their products (the Classic Vibe range in particular) are every bit as good (if not better in some respects) than my Made in Mexico Strat that says "Fender" on the headstock.

For sheer versatility, I would not overlook the Epiphone Nighthawk, and the 339, along with the 'Kat. For Fender products, you just can't go wrong with a Highway 1. They're built like a tank, have great necks, and sound fantastic. They are being discontinued in favor of the American Special line, so you might be able to find a good deal on one. I would look at a Strat and a Telecaster. A good Tele can do everything you would want it to do and then some.