Lokking for opinions

There are no differences in the requirements for a home theater sub versus a stereo sub. Either one should be able to reproduce low frequencies at reasonable volumes with minimal distortion.
The whole concept of there being differences is a marketing ploy, not unlike the phrase "Digital Ready" (as though digital source material had different system requirements from analog source material).
Build a good sub, and you'll be happy with it for either use.

Grey
 
A subwoofer is probably the easiest type of speaker to build. Additionally, a sealed subwoofer is probably easier than any other type. If this is your first subwoofer, you'd probably be happy with one of the readilly available 10" or 12" sub drivers, in a small sealed enclosure. The size of the enclosure could range from 1 to 4 cubic feet (actually, you could build it larger, but you should probably try something in this size area first).

If you're looking for a kit , check out 'http://www.adireaudio.com' (Shiva), 'http://audioc.com/diy' (SV10 and SV12) or 'http://www.partsexpress.com' (Titanic). They all have kits, based on the listed drivers, although only Parts Express seems to have the cabinet available as a kit. There are many other good sub kit vendors out there (including http://www.madisound.com); the ones I suggested first build their own drivers (OK, they have them built to spec).

If you're looking to do the entire thing from scratch (it's not much harder), the first step is to get some speaker modeling software. There is quite a bit of free software for this purpose. I like WinISD ('http://www.linearteam.dk'). You plug in the driver you intend to use (there is a very complete driver database with the software), and the size of cabinet. For a sealed enclosure, most people look for a system Q that's below 0.707 (but rarely below 0.5).

Once you've decided on the volume, you need to figure out what shape you want. Due to the low frequencies that a sub deals with, you don't usually have to worry about standing waves. This allows you to ignore the 'golden rule' cabinet proportions, and use a shape that works astheticly. Be sure to allow plenty of space (depth) to mount the driver. They are usually fairly deep.

When you get to building the box, use plenty of internal bracing. As the box gets smaller, this becomes less important. The idea here is that the walls of the cabinet shouldn't flex at all. Common construction materials are 3/4" MDF and 3/4" Baltic Birch plywood. If the enclosure is large, it might be a good idea to use thicker material, or two layers. The corners should all be caulked (silicone works well here), to ensure that there are no leaks.

NOTE: Baltic Birch plywood is NOT normal plywood (which makes poor cabinets). Baltic Birch plywood is made of hardwood, and has may thin layers (almost twice as many as normal plywood). It has few internal voids, and is quite ridgid.

In a small subwoofer (without a 'plate' amp), a plastic 'cup' is used to house the binding posts. In a larger sub, the cup would break, or flex excessively, and a different method would have to be used.

If you wish to use a plate amp, the same companies that have the drivers also have the amps (check out 'http://www.apexjr.com' too). A plate amp screws into a rectangular hole in the speaker, and has either low-level inputs (RCA jacks), or high-level inputs (binding posts). In the former case, you would need an RCA cable going to your receiver or preamp. In the later case, you would run speaker wires from your receiver/amplifier to the subwoofer, and another set of speaker wires from the subwoofer to the speakers.

Reguardless of which path you choose, you'll be amazed at the improvement in bass, and you'll learn a lot too. Be warned, a subwoofer is heavy, and it may easilly take several weeks (elapsed time, not work time) to build.

God luck