I don't like Epiphone myself, used to have one and thought it was good untill I tried out some of the more pro guitars in the local shop. Once I went Ibanez I could never turn back - try an RG series, make sure it has Dimarzio pickups. The sound and playability of their more pricey models are amazing. For sweeps and really fast lead I find the smooth neck (as opposed to the varnished or painted finish) a big help, stops the thumb from sticking on the back of the neck. Ibanez come with an outstanding trem system that never goes out of tune even after upward harmonic shifts and dive bombs.
If you don't like Ibanez, how about an ESP? How much are you willing to spend? Consider a really good guitar an investment, you may never change it so its worth splashing out.