Wow this thread is *perfectly* timed. I have a 2001 civic and I was looking to get a new deck for my car and get rid of that crappy factory model.
Buying a Radio
Definitely don't buy from BB//FS most of the stuff there is horribly overpriced unless there is a big sale. I'm still doing a ton of research but one place I found that was really good was
Crutchfield. Wow I just checked out the american site, apparently 129.99 gets you the trim kit, wire harness and install guide. That's a really good deal.
Installation
If your like me and are just installing the radio and keeping everything else stock (no sub, factory speakers) then I would try doing it yourself and saving the cash. If your driving a fairly well known car there is probably a radio installation instructions posted with pictures. Check it out and see if it's easy enough to do, chances are it is. The wiring harness makes things nice and simple, just plug and play especially since its color coded most of the time, plus you can reinstall the stock radio since you didn't cut anything.
Features
As for features, if you have an ipod it might be worth it to find a model that has a ipod cable since it can feed information directly, plus you can use your radio // steering wheel controls to change songs (definitely worth the price). I would look at getting HD radio if you are in the united states as its pretty popular there.
The model im looking at Kenwood KDC-MP442 basically does everything I need and includes the kit for 149.99 (it's 149 for Canadians to get the free stuff).
Edit: What's your new car? Congrats!
Eugh I just looked a radio install for my car on yotuube. Wow that's going to be fun, I have to remove the center console to get to my dash.