Don't worry about the head unit, it's a fine unit and will definitely get you better sound quality.
However I wouldn't get those speakers either no matter how much i love alpine product. I wouldn't even get the Type X's. Their PDX amps are sweet and would work well in your car, which is sweet by the way.
Some suggestions for door speakers that would do that car justice:
The Rainbow Line, check out all of their component speakers, they will all easily take 150 watts and sound great doing it.
Rainbow (germanium line and up will blow any alpine set out of the water, and germaniums are very affordable)
I am very much impressed with my Phoenix Gold RSD's which have been mentioned on here a couple times already, they are very much worth the money.
Phoenix Gold RSD
There are a lot more, but those would be my top choices, also check out Hertz, and Polk Components, they are also known for quality.
Another big thing would be to apply sound deadener to your front doors behind the speakers. I know the Evo already has doors that are already a lot more acoustically deadened than most doors straight out of factory, but they could still use sound deadener to help your mids really come alive. And using an amp is a must for replacement component sets.