$200-300 is really not much for good sub - musical subs are much more precise than a typical HT sub and thus more expensive.
Above mentioned NGX is not terrible way to go at this budget, but as also mentioned you probably should save a bit more.
Good Sub function is vastly underrated, and good sub cost good money. My mains rated down to 30hz, yet after I've added an expensive PA-120 sub and some basic calibrations - the whole system started to sound 100 times better.
If you have an skills and change to build your own box, this opens up whole new world and would allow you to build simply an amazing sub for very little green
This driver:
HT18 18″ Subwoofer | Stereo Integrity in a 3 or 4 cuft box and a couple of hundred for pro-amp and you would be in sub heaven.