Integras are very hollow cars!!! And the Type R has a lot of weight taken out of the doors compared to the other Integras, so if you put in a decent quality split system, you are bound to get a lot of door rattles when the bass comes in! You could fix that with a sound dampening kit but it will add a fair bit of weight onto the sides of your car.

I have a GSI with an alpine Type R split system and when i'm playing a song with decent bass, the door rattles like hell! You could do a nice system, but i would suggest not putting speakers in the doors, but instead having a custom set up next to where your legs are. Then mounting the splits on the dash. Also installing brackets into the rear speakers as the stock ones aren't too good (you can only fit 6" speakers in the rear, not 6" x 9"s).

Subs shouldn't be a problem concealed in the boot, and amps under the seats, should make for a decent sound system. If you want to do it right, first time, then get a custom install for everything, to make sure it sounds good, and doesnt add too much weight.