First of all, "clean deep bass" may be relative to each person so be prepared to come across different opinions. Here is mine.
Sound is suppose to be clear and balanced at all levels with solid bass response within the cabin. The more excessive external "boom" the more imbalanced your sound will become. Thus, a high quality 10" sub in the 300-500 RMS range is perfect for solid clean bass in a Civic. A 12" sub, like XpL0d3r suggested, will sound deeper but need a bigger box than a 10". I prefer and need to have trunk space, so I custom built my sub box to fit in the corner and have the optimal cubic footage for the subs performance. I also custom fabricated trunk panels for easy access to the spare tire area with the sub installed. I had another sub box roughly .1 cu.ft. larger than this box but this one made a bigger than expected improvement in bass response. So if you dont choose to build your own box, make sure whichever you buy is within specifications of the sub you choose. Not everyone needs to go the route of customizing, but it may come down to your needs.
FYI, only factor in RMS wattage. Max wattage is virtually useless unless you're building a competition type set-up.
Sub Box Volume (cubic footage) = H (height) x W (width) x D (depth) divided by 1,728
Do you have any brands of subs and amps already in mind? You cant go wrong with JL Audio subs and Alpine amps.