Alright, I'm still learning about suspension (I don't think anyone ever stops learning), but first of all I would say you don't need 17x10. Unless your pushing some large power numbers. Your probably having traction problems because you've got some cheap tires right now. If you get 225 all around you should be good. 225 tires will look great on some 17x7.5 wheels. By keeping the wheels at a narrower width, you won't have to have as high an offset. That'll give you more room for your coilovers. It'll also keep your suspension geometry in tact a little better. For some good brakes, try some 300zx brakes. You can research that here and find lots of information, just read the sticky in the technical formum (I have a feeling I'm spelling everything wrong). Just my opinion, but if your not going to be getting any track time, then a nice expensive set of coilovers is a waste, but hey, just my opinion. If you want some coilovers you've got lots of choices. Most people here will recomend JIC or TEIN. I don't have any experience with any of these yet, still saving.

As far as clearance issues go... from what I hear its just kind of a guess and check thing. You can measure to find the offset needed for wheel to clear the coilover, I think you'll probably need around a +35 with 7.5 wide wheels. But if your wheel of choice will clear the 300ZX brakes is hard to tell until you've got it all on there... that sucks, but I think thats how it is.
If anyone finds any mistakes in this, correct me.