Good Subwoofer recommendations

I'm looking for a good Sub for my existing HT system.

There are so many types like Sealed, Ported, Cylinder, Bass-reflex, etc. & it's a bit confusing to determine which one will be better. Also, does type of speakers or Amps I have can impact the decision?

My budget is around $1000 & I prefer getting a used or refurbished rather than new.

Current setup:
LRC Speakers: Tyler Acoustics Linbrook System II
Surround Speakers: JBL S312
Amplifier: Parasound Halo A51
BD Player (cum PreAmp): Oppo BDP-105
Room: 16x18+ with ~40% open walls, so sound can bleed

Thank you in advance!
There is a Bag End Infrasub 18 for $895. That sub was a review winner many times for HT. Probably can't go wrong with that. With 40% open walls you will need the size as well.
I think SVC makes great lower cost subs. A critical question, though, is if you are just going to be doing movies or will this be your TT/CD/SACD system as well? If you want it to do everything, I strongly recommend a sealed set of subs. Ported subs are just too slow, unless you want to do some serious modification. In my HT room I'm using a set of sealed subs and have found it a fair trade off to the one ported sub that is found in so many rooms. I do have a 15" sub in the garage/gym that is ported, but even there I had to modify the port and use a lot of Marigo speaker dots to get it to be listenable. I have to say, though, exercising to a 15" sub is motivational!
Rythmik has their E15HP in matte black on sale right now for $1024 plus shipping. 15" Servo-Feedback woofer, 600w amp. Best deal in subwoofers.