In your stereo you want to look for preamp outputs (low voltage). 4V is common, but 5V is better. Each output will correspond to a speaker channel. You will have to determine what speakers will be driven by your amp. Will it just be subs? The front and rears? Or all of them? Whatever you determine, you will want to look that your head unit has the corresponding preamp outputs and has an internal amp to power whatever speakers will not be driven by the amp.
The preamps are simple RCA connections that go straight to your amp and all head units and amps have wiring diagrams in the instructions. They usually have sample layouts with different amp and speaker combinations also.
Just a word of advice, don’t buy from Crutchfield. They do have good customer service, but you can find the same equipment (brand new just like they sell) for at least 40% less at other online dealers. I like to use
www.onlinecarstereo.com for example. Crutchfield’s site is good to use for research also.
As far as brands, Alpine, Pioneer, Pioneer Elite, Kenwood, Kenwood Excelon, and Eclipse are all very common good brands of head units. I have not stayed on top of current amp and speaker technology. Someone might have better ideas of what to do there. As a general rule, component speakers will sound better than the combination speakers (ex. 2 way, 3 way). Component sets will come will filters to keep the correct frequencies going to the speakers that are optimized for those frequencies. For example, you won’t be sending your low bass to a high frequency tweeter. Some amps have these “crossovers” or filters built in also.
I guess the most important thing would be to set your budget. Then find the equipment that interests you and ask questions about it.
There is a ton to know if you really get into it and this might create more questions than answer them, but keep asking the questions.
Let us know more about how many speakers and what type you intend to run.