I second the Velodyne Optimum 8. That's what I have and it is highly musical and the auto room correction is a must for a music sub. Also, I think a smaller woofer will integrate better with the main speakers. With the OPs budget they would need to find a used one.
System
I'm trying to assemble a decent but not overly expensive system. I have Totem Rainmakers, and Triangle 202. Currently I use an inexpensive Yamaha sub. It has been suggested that I get a "fast" sub. I don't know what that means. My budget is limited to $200-400, new or used. My room is about 12x14 Any suggestions? Thanks in advance.