The head unit will supply enough power to the stock speakers. You will not need to amplify the signal. Doing so will likely blow the speakers. If you replace your stock speakers with higher wattage speakers, you may need an amp with the channels to power these.
A one or two channel (bridgeable) amp is sufficient for the subwoofer(s).
When I had a system, 2-500w 12 inch subs with a 1000w single-channel amp, and 4-100w 6x9s with a 400w 4-channel amp was much more than enough for me. But, I guess this can be subjective.
I used a cheaper line of Rockford Fosgates for the 6x9s. They sounded a little tinny, but were loud. I used 2 Jenson 12s in a bandpass box, also very loud (turning system up was like getting a message), but not as deep as a 15" could have been.
If you're just going to add the head-unit, subwoofer(s), and leave the stock speakers in, you need a wiring harness to hook up the head-unit to the stock speaker wires. The wiring harness should come with a diagram. Then you will want to run one or two RCA cables from head unit to the trunk into the amp. Then run a large amp power cable from the battery to the trunk somehow. Depending on the car, running the cables to the trunk can be a little complicated, with plenty of opportunities to mess stuff up, so you may want to have a professional installation from a place that has a good reputation.