I also used to watch DBZ a lot when I was younger so the idea of having ULTIMATE POWER BEINGS still excites me (although I am open to the idea of shows that don't contain energy blasts, psychic hands, or god-like beings). I'm not into Naruto, though, so please don't suggest that.
Bleach.
There, I said it. (It wasn't so hard guys, why do you always want to be elitist whenever someone asks for anime suggestions?)
It tries to do a lot of stuff at once, but what you described is what the show does best. There are a bunch of episodes, so you'll probably end up watching them all in rapid sucession and get sick of the show pretty quick, but it's a good ride while it lasts (for one thing, the bullshit it tries to pull is a lot more bearable than the crap you get with Naruto, although it strikes some strong similarities at times).
Oh yeah, and out of a lot of dubbed animes, I like the dubbed version of Bleach more than most. (Like most dubs, it has it's problems, but putting the guy who did Vash from Trigun as the main character was a suprisingly good fit.)