A component speaker just means its two seperate speakers, tweeter (normally smaller and put high on the door, at shoulder level, and a midrange, larger and placed at the bottom of the door. These tend to be more expensive but will sound better. The alternative is a 2 or 3way speaker which is the tweeter mounted with the midrange, so that they both go in the door. You have a couple of options with your 4 main speakers. You could let the head unit power these speakers, which in that case you will end up getting something like 20-24 watts rms per speaker (dont bother looking at peak watt power, always look at rms power). Or you could buy a 4 channel amplifier to power your speakers, this is a popular option, although somewhat more expensive, it will make the music sound much fuller and really give you the power you need.
If you are buying a subwoofer, I would suggest something practical, one or two 10 inch or 12 inch woofers, this will not only keep the installation simple, it will save on your wallet. I have one 12 inch woofer in my trunk, but it is getting 800 watts rms. Some people have 4 12 inch subwoofers in their cars, each one getting 200 watts rms, do the math, its cheaper to just get one good woofer that will make a lot of power.
Some people buy capacitors for their systems, which is kinda like a second battery, only a lot cheaper, and easier to wire. I have a 1 farad capacitor for my system, and it helps so that my lights dont dim when I am listening to techno, or 50 cent. The general rule of thumb is 1 farad per every 1000 watts rms of power your system needs. So if you put together a smaller system, you would only need a 0.5 farad capacitor.
Stick with key brands when buying a system, rockford fosgate, audiobahn, jl audio, sony, dont buy brands like profile and rockwood, because it will end up sounding like you bought it at the flea market.