The way I did it is I ran all new wires to the door panels from the trunk, and now I have just amps powering speakers with the head unit only having power, ground, remote turn-on (antenna and amps), and RCAs. However, you should be just fine using your stock wires.
I say you should have a set of plates made to fit the 4x6 openings but then have a hole in the center for your tweeter. When you get component 6 1/2 speakers, they will have one input of + and -, and then there will be a crossover box to make sure the large speaker and the tweeter have the right signals going to them. Match up your door or tweeter wire colors to the wire colors on the back of the radio (do this once you get your adapter harness, and it'll make too much sense then), and use those two wires for the crossover box only, then run wires to the tweeter and the large speaker, and you're set in the front.
In the back, use the regular speaker wires for your new 6x9 speakers. See how that sounds, and I think it'll sound excellent. If you still feel like you need more bass, you should then get a woofer in the trunk. I don't really feel like I should have subs with my set of speakers (10 with tweeters counted individually, and 12 with subs counted), but it does help to have them with filtered-out bass for the cleanest possible sound at high volume levels. I really like it, and I think it works well for me, but I know there are more ways to achieve quality sound in a car and the subs just aren't necessary. Plus, this way saves you money!
I like all the suggestions made so far, and I simply wanted to make a wiring suggestion on the front speakers when all of a sudden this large post swung by. Sorry about that.