Looks like you've done some research. DIY is definitely the way to go, especially in the subwoofer department. You can save yourself a lot of cash.
Commenting on what you said above, here's my take on it.
Easiest to build, can generally be the smallest enclosure, but can also be just as big as ported / horn subs if needed.
Has potentially the lowest frequency extension, due to the air spring of a box acting like "insurance". One can use multiple sealed subwoofers with or without subsonic filters, and with a bit of eq, get a flat frequency response down under 20hz, to the single digits. There is plenty of movie content below 20hz (where we stop hearing it), but it is up to you whether or not you want to pursue the last few octaves.
"Generally" the most power hungry of the 3 enclosures.
Based on the box size, you can "tune" your box to a certain frequency, using a slot or pipe as a port. A port will give you free volume at the port frequency, sometimes up to 2-3x louder then the equivalent sealed subwoofer. The disadvantage, is ported subs unload under the port frequency. So if you made a ported box tuned to 20hz, you would use a filter at 20hz or just below to stop the driver from being damaged. This means you won't get much more output under where the filter is activated.
Ported boxes can be made huge (10-15cuft is a good number), to give you an increase in output across the board, since a filter is being used to stop overexcursion, we can take full advantage (and sometimes more) of the driver's power rating.
They can also be tuned low, around 15hz if you desire, to give you a good balance of low frequency extension that a sealed box would have, while keeping a bit of output gained from the port.
Next to horn subs, they generally get the loudest, so if you have a big space to fill with bass, or can deal with a huge box, they are an obvious choice.
A good design to look at is the "Martysub" designed by Marty and LTD02 on the forums. It's 12cubic foot ported box tuned to around 17hz, designed to work with multiple different 18" sub drivers.
Gives you the most output for the $$, they are the most sensitive of the 3. This means with the equal amplifier power used, they should play louder then the equivalent sealed or ported box (all things equal).
They have a "corner" frequency, similar to a ported subwoofer. Horns should almost always have a subsonic filter to stop super-low frequencies from coming through underneath the corner frequency, and damaging the driver... just like a ported subs port frequency.
Horns are big, usually bigger then ported or sealed subs. They require significant size in order to push the corner frequency lower in the bass spectrum. So if you want a horn that plays as low as a sealed sub, or a large, low-tuned ported sub, prepare for something that's HUGE.
Most difficult to build, has many bends and folds.
A good horn design that doesn't sacrafice much extension or volume is the THT (tuba home theater) design by Bill Fitzmaurice, and the F20 (design by Lilmike).
Everyone one of these should sound "musical", if setup properly and used within their operating capabilities.
As far as what to go with? Well that depends on your goals.
Do you want to spend $500? $5000?
Do you want low frequency extension to the single digits? Or is 20hz suitable?
Do you have space to fit a 10-15cuft box?
Can you fit multiples in your room? Multiple subwoofers improves bass response by smoothing room modes.
Giving us an outline based on these/your criteria, and we can better recommend you something.
Hope this helps.
Edited by Thatsnasty - 1/12/14 at 4:56pm