Personally I'd tune between 32-34. It will get down to about 26-28 nicely and still do well up to 45-50 hz (Depending on where you have your cutoff set at).
Regarding mid volume and upper volume limits would depend on what you are running for the front stage of your set up (Tweeter, mid range, mid bass). Too much power to the subs will drown out anything up front. This could be a good or bad thing. The amount of space that you are listing seems quite small and really limits the subwoofer choices and the amount of output you will get. I agree with JoeX a trunk build will be ideal and gives you the room for a decent sized enclosure backed up with a decent power amplifier.
For types of subs there are many. For your budget range of $500-700. I'd say go with brazillian board amp. They tend to be cheaper but still put out good power. For subs that's a tough one. If you are sticking with the space you have given, then your only real option is to go with a slim subwoofer but that limits your power handling. If you go with a trunk build, there are many options to choose from that are between $200-250 (each) and have decent power handling of 500-1000 watts rms .