In my opinion, the first really good "this is what bass ought to be like" sub starts at $500 with the Rythmik FV12. If there's any way to save up for that sub, that's what I'd recommend doing.
Below that, you're forced into compromise. If you're mostly after the rumbles and booms in movies, and you're willing to give up some control and "tightness", the Elemental Designs (edesignaudio.com) has the A2-300 and A2-250 in the $350-$415 range - and lower if you can find a B-stock.
The HSU STF-2 is my "go to" for a $350 "music is important to me" sub. Won't hit super low, but it's nice and clean and accurate and pretty darn capable all around.
Outlaw Audio has sister models to the HSU brand subs, so it's much the same story as HSU.
Below that, I say you have two options:
1) wait and save
2) spend as little as possible so that you can save up that much faster for the $500 Rythmik FV12 or something even more expensive than that!
If you go with option 2, I'd say to only do it because you just "gotta have a sub, man!" and you're going in with the full knowledge that this isn't going to satisfy you for long and that it's a temporary sub that WILL get upgraded!
That said, my "go to" is easily the Onkyo SKW-204 . $120 at Amazon and under $100 if you do a google product search and are willing to risk an unauthorized retailer.
The Onkyo SKW-204 always manages to put a smile on my face whenever I hear it. It's got no right to sound as good as it does for its price

I'd take the Onkyo SKW-204 over any other sub that costs less than $350. Not because it's literally the best under $350, but because it's so cheap and actually pretty good, which means that spending more might get you a little bit better, but not much, and IMO, not worth any extra $$$ because the SKW-204 will let you save up for a "real" sub that much faster!
It's a value bet for me. So I say to save up for the $500 Rythmik FV12 if at all possible. Pick between movie rumbles or accurate music with the $350 eD A2-250 or HSU STF-2, respectively. And if you can't muster those and you just GOTTA have a sub in your system somehow, then skimp as much as possible on the price, but still get rather amusingly good sound from the $100-$120 Onkyo SKW-204 so that you can save up without sinking hardly any money into this "temporary" sub!