Ok, if you want to run a set of components, you will need an amplifier, cause I think the alpine pushes 27w RMS x 4, yes I know it says 60x4, but thats peak power, you have to look for the RMS power.
If you want to run your speakers from your deck, then get a set of coaxial 5.25 for the front and some 3-way for the back, I you like alpine, their speakers are good to, that will sound nice, and should be ok, for most of the people.
But if you really want quality and power, then get an amplifier
Your deck is really nice, I think it has 3 sets of RCA outputs, yes the red and white cables in the back.
Search for a good amp in the web, alpine amps are good, but there are sooooo many other brands, well order the amp, and then go get it profesionally installed, if you say you dont know anything about car audio dont try to do this, learn first.
You should search for something like 50w RMS x4 for running your comps, this should give you nice sound and power, the alpine type R componnets are good, but there are better ones, like boston acoustics, infinity, crystal, etc, just go to your local car audio shop and listen to the speakers and chose the one you liked most.
6.5 comps in the front should be ok, maybe a good pair of 3-ways for the back, or another set of comps.
Then if you want even better sound go get another amp, (a 2 channel know) with something like 100rms x2, and get a good pair of subs, for sound quality get a sealed box, for high volume, get a ported box. Again get this one professionally installed}
and again the alpine´s type R are really good subs, other good ones are ID, JL, etc
hope that makes you an idea of how you should get started