Gunbei -
There is a trade-off relationship between efficiency, bass extension, and enclosure size (some money gets traded off as well).
Most people want the maximum bass extension and loudness in the smallest possible enclosure, which means you have to trade off lots of efficiency. Since very powerful amplifiers are relatively inexpensive, that makes sense, right?
Well, maybe not. You see those compact, ultra-long-throw, low-efficiency woofers suffer much more from dynamic compression than a higher efficiency woofer does. Which doesn't really matter on movie soundtracks, but it does matter on music. In my opinion, for music you need a sub with a fairly efficient woofer to minimize dynamic compression. The only way to get deep extension and good efficiency is to use a big box. This is what I've gravitated towards after years as an amateur speaker builder.
Also, sealed boxes are almost universally considered to have better transient response than vented enclosures, but there are vented alignments that rival the transient response of a Qtc = .5 sealed box, yet give you better extension for a given enclosure size.
And the thing is, higher efficiency woofers (for minimal dynamic compression) naturally have parameters that are best suited to vented enclosures.
OF course, if you want a sub primarily for movies, then you'd want a bass alignment that maximizes output rather than transient reponse.
For music, if at all possible, I suggest stereo subs. The reason is, very low frequency out-of-phase information is present on many recordings, and gives a sense of the size of the hall the recording was made in. This is picked up by the widely-spaced microphones. When the bass is summed for a single subwoofer, that out-of-phase information is cancelled and lost.
I'm a dealer for a very musical line of woofers, namely Lambda Acoustics (www.lambdacoustics.com). I've been building speakers as a hobby since the late 70's, and these are the best-sounding large woofers I have found. They are fairly expensive and tend to be of higher efficiency than most woofers, which means a bigger box for a given -3 dB point, but their dynamic impact is very lifelike.
If you're interested, let me know what you can live with in the way of box size, and I'll let you know what Lambda might have to offer you.
Best of luck with your project!
Duke