LarryJ,
Diamond Audio are decent speakers, you'll enjoy them. Are they component speakers like the stock ones (seperate tweeter) or the coax type? What is their power rating? If it's only 45 watts RMS, then you should be O.K. with the stock amp. Aftermarket amps make a big difference in sound quality. My logic is if you are going to change the speakers, why not change the amp at the same time and enjoy great sound instead of good sound?
The amp I used is one of many that will work fine. Actually, you might be better off with an Alpine amp, they make one very similar to the stock one but with more power, and can actually fit in the stock location. If not, under the driver or passenger seat is a good location and running wires to it is simple.
I ran all new wires because I wanted to maximize power and minimize noise. Also, I didn't want to cut any stock wires, so since I had to run 1 new one (the remote turn on wire) I figured I might as well run all new ones. I also ran 12 gage speaker wire. The stock wires will work, but not well with an aftermarket amp. You will also need RCA's going to the amp. You can use a line level converter and tap into the stock wires, but noise is an issue, and you have to cut into the stock wires. You also have to consider that the stock speaker wires are incredibly small. 16 gage is the minimum I would recommend for car audio system. The voltage drop of anything smaller is significant.
However, if you are looking for a small but noticeable improvement in sound quality, stick with your plan of just changing speakers. If you go beyond that, you might as well go all the way.