The new Kenwood included with the Civic is good, thank God its gone beyond delivering the flat sound plagued by the past Kenwood HU's. However I'm going to suggest you change the head unit completely if you want to upgrade it.
I had Bose speakers with the stock head unit (with a premium 4 channel AMP), but the unit just couldn't give them the right juice. I tossed it out and put in a JVC DVD player, best decision I ever made
Anyhow, if you're going to add a woofer and WANT to keep the stock HU, I suggest:
Adding two amplifiers, a 4 channel and a 2 or monoblock.
Change the speakers to something like Alpine components
Add an Alpine or Soundstream woofer. JBL is also good.
Thats my honest advice, a woofer with the stock speakers is a waste of money
Good luck!