When it comes to subs, the room tells you a whole lot about what kind of output you're going to need. A sub doesn't "know" that only a section of that room is designated as the "theater" area. It just tries to pressurize the entire open space!
You've got a pretty large space to fill - technically on the larger side of a "medium" sized room at over 2500 cubic feet, but under 3000 cubic feet (I'm assuming the ceiling is around 8 feet since this is a basement).
To me, "proper" bass starts at $500 (plus about $60 shipping) with the Rythmik FV12. As I've said in many other threads, it is the least expensive sub that doesn't have any obvious compromises to any part of its sound. Below that price point and particular model, you're making some sort of obvious trade off. Either the sub will not play the deepest bass (the below 30-35Hz stuff), or it will play low, but give up "tightness" in the transient response, which leads to a "less quick" sound with notes sometimes blurring into each other, or just less accuracy or higher distortion.
The FV12 gives a very nice balance of all aspects with no real weaknesses. If you're looking to keep your subwoofer budget as low as possible, that's where I would point you.
The FV12 will certainly not have enough output to play at reference volume levels in your room. But you've already said that you aren't looking to blow the doors off or anything

The thing is, when you have low distortion, things do not SEEM "loud". With our human hearing, we strongly associate distortion with "loudness". In strict terms of sound pressure level, a sound that is technically quieter (lower dB reading on an SPL meter) can still
seem "louder" to us if it has high distortion vs. a sound that is technically louder (higher dB), but lacks distortion. So with a nice, clean sub like the FV12, it's easy to keep turning it up!
Thankfully, the FV12 is very well engineered and will not damage itself or go into crazy high distortion if you crank the volume. Thanks to its well made limiters and filters, it will simply play as loud as it can and then politely stop getting any louder
With all of that praise out of the way, I would still be far more comfortable with higher output capability in your room size. With floor space at a premium, there is no question that SVSound's cylinder subs take up the least amount of floor space while delivering true linear extension all the way down to 20Hz (or lower), and much like the Rythmik subs, an "unbreakable" amplifier that will simply and politely refuse to play any louder than the sub can safely and cleanly play. The PC12-NSD is obviously more expensive than the FV12. It is also a more capable sub. So that's where your extra money is going

It can play a bit lower and it can play a bit louder. It's perhaps just a hair cleaner too, although it's really too close to call on that front. We're not talking monumental differences here, but they are definite improvements for the higher price tag. And if you need the floor space, nothing beats the 16.5" diameter cylinder form factor
It is important to know that it makes PERFECT sense to spend proportionally more on your subwoofer than any other component in your system. Subwoofers have a difficult job. They are also what takes your experience from mere "surround sound" to "theater" quality! When we think of the thrill of movie theater or live concert sound, it really is the deep, strong, tactile bass that completes the experience. It's the thing we most often lack when we try to recreate the experience at home! So don't even think about skimping on the sub. Go without surround speakers. Go without a center speaker. But don't cheap out on the sub! If you're going to "splurge" anywhere, spend extra on the sub. It'll pay you back with a great sense of enjoyment than anything other than your Front L/R Main speakers!
To be perfectly honest, in your room size, if you were able to afford it, I'd be springing for an SVSound PC12-Plus or a Rythmik FV15HP! But then again, I love reference level bass and find it hard to accept anything less than an SVSound PC13-Ultra these days

Actually, scratch that. I find it hard to accept less than A PAIR of PC13-Ultra

$3500 on subs (after I get a pair of Auralex SubDude isolation risers to put under the two PC13-Ultra cylinders)? Absolutely! Money well spent
