Subwoofer: How low should I go?

your neighbors won't like it...guaranteed....no matter what you get...bass waves penetrate just about anything. That said I'm using a von Schweikert VS1 which you can pickup on Agon for well under $1000
Larry

Even if the subwoofer goes no lower than your main speakers, it will do it with less effort (distortion), and will relieve the main speakers of the task of LF reproduction, and that will make the main speakers better in the other part of the frequency range.

Go with that sort of sub. The lower frequencies are the ones that travel. If you had a sub that did 20Hz your neighbors would shoot you or get you evicted.
38Hz is a figure. The sub DOES reproduce notes below that, but at less volume. 38Hz is likely the 3Db down mark, a standard measurement.
Even with a sub that goes only to 38Hz you should be careful in placement, as the resonances could get ugly in a neighbors apt. I am in an apt in a 'over 55' building, so I cannot make ANY noise or be evicted. So I have my sub on a 2" thick concrete patio slab on rubber feet. It really keeps the vibration in my apt instead of my downstairs neighbors.
I like a small sub because it gives a normal bass sound at low volumes. So in a Jazz quartet, you get a true bass note from the bass. Nice.

If your listening room is small, then it will not effectively hold a low frequency sine wave. You would need a medium to large room to get the lower octave that some subwoofers produce well. That being said, I do believe a small subwoofer integrated into a two-channel hifi system can work well in a small room. I think achieving around 40 hz in a small space is possible without loading up the room. Also, some of the better subs out there come with a room equalization microphone that helps get rid of the major room modes which might be an issue in a small room.

I recently added a JL Audio Fathom F113 to my two channel system which is in a room that is 40ft X 25 ft with 11ft ceilings. This sub transfomed my system in almost every way for the better.