You should be able to build a box in the 3 to 3.5 cuft (internal) range.
I would suggest a sealed sub if you don't want to wake the neighbors (as often anyway). But for HT ported is the way to go. If you plan to get a house anytime in the near future go ported, you will be happier in the long run. Passive radiator is out due to budget.
I would recommend the 12" dayton titanic MK-II available from parts express or the AV-12 from stryke audio for your sub. You can go sealed or ported with either of these in that size of box. The dayton does carry a 5 year warrenty if you are prone to blowing things up. The shiva is also nice I have heard, but can bottom out in ported HT applications; As will the titanic MK-I. If you go sealed you will be happy with any of the subs I listed. These will also all mate well with the PE 250 watt amp I posted above.
Amother good amp deal can be found at
www.Rythmikaudio.com 350 watt plate amp with variable rumble filter and bass boost for $140