Perfect, I've got an Alpine as well. I think they give great sound quality. You really dont need to amp the speakers then, I'm sure you'll be happy wiring those up to the high-levels outputs.
There's more of a difference between component sets and co-ax speakers. Co-ax speakers come in a variety of styles, usually two-way, three-way, or even four-way setups. Basically, one signal wire is connected to the speaker right from the deck, and the speaker divides the frequency to the appropriate locations within itself. The three-way speakers will probably have two tweeters and a low, or a tweeter, mid and a low. A two-way will only have a tweeter and a low.
Component sets are different in that the signal wire initially goes to an EXTERNAL crossover, which then divides the frequencies up, and sends the appropriate signals to the different speakers (still a tweeter and a mid/low). Most people like components over co-axs because they tend to be adjustable and they do a nicer job of divinding the frequencies, thus a nicer sound.
The idea behind both setups is that you cant send low frequency signals to a tweeter, and tweeters handle high-frequencies better than a larger speaker would.
If you decide to get co-ax speakers, three ways will probably provide a better range of sound, because each component of the speaker can play the frequencies it excels at.
However, if you're gonna replace all of your speakers in your runner, and you use varying sizes, you could probably stick with two-way speakers. If you only have two speakers in your entire vehicle (like my old camaro) then three-ways make a little more sense. All of my speakers are two-ways (including the component set-up in the front). I have 5-1/4" components in the front, 4" in the rear doors, and now 6x9s in the rear. I'm happy with the sound quality. I get lots of highs, and enough lows, considering I dont have a sub.
I dont know if you're going to tackle the install yourself, or if you're gonna pay someone. But you should try to find a place where they dont mind explaining the stuff I've been trying to explain here. I've never dealt with Best Buy, or Future Shop, or any other chain store for my audio, only because I find I can never get the service I want. Just make sure the place you go is reputable, and if they dont wanna spend 10 minutes with you to help you decide what's best for you, like asking what kind of music you listen to, and what kind of car you drive, then walk away.
Good luck man