I want to get a processor...Where do I connect the surrounds

If it is for movies only, an 7 channel amplifier should be fine.
If use it for stereo also, a stereo amp or 2 mono blocks + an 5 channel amplifier, featured with auto turn-on function is a plus.

how do you guys run the center channel surrounds and back surrounds. Another separate piece?

I use a Denon receiver as a processor, Sunfire Symphonic Reference Amplifier to power front left and right speakers and a 5 channel Sunfire Cinema Grand to power the center channel, side and back surrounds.