I'm using the SVS SB2000 Pro with my DQ-10s... highly recommended! A new one is a little more than your limit, but I'm guessing the SB1000 Pro would work just as well depending on your room size and how loud you listen. And the SB1000 Pro is within your budget.?
Dialing in a powered sub can be a pain in the butt. But SVS has a smartphone app that allows you to do all the adjustments and settings from the listening position. Makes set up and integration soooo much easier!?