If the car is not being driven in temperatures below 50 degrees F, then high performance summer rubber would be the best option. Since you indicated "daily driver" (although how is a daily driver then not driven in the winter?) then a tire with high treadwear rating like Michelin Pilot 4S would be preferable. You won't be winning any races but neither will you be replacing your tires every 10k miles. You wouldn't be winning races with bag-suspension anyway.
As for wheels, I don't think anyone can answer that question for you. You will want wheels that are as close-to-stock offset (+53) as possible, between 7.5" and 9" in width, and preferably as light and structurally sound as possible. The bolt pattern on the 2004 STI hubs is unique among STIs at 5x100.
Welcome to Club BTW!