I chose SPL, low end extension, tactile response, and low distortion. I believe they are all important and linked.
A high SPL, coupled with low end extension provides the tactile response that makes movies engaging, at least to we HT nuts.
Low distortion is important, obviously, because a subwoofer that outputs distorted sound is less than desirable. Distortion detracts from SPL, extension, and tactile response and can result in muddy and undefined bass.
Compression isn't a real big deal to me as long as it is not excessive.
Size really doesn't matter to me as long as I have room. My DIY sub is very large, about 3ft cubed. It is extremely potent and goes very low with the Atlas 12" driver.
Anyone who has seen pictures of my subwoofer knows that looks aren't high on my list.
I never got around to veneering it. It is plain MDF with glue showing. Besides, when I have a dedicated theater room where it will usually be dark no one will see it anyway.