jlee, BIC America subwoofers might be cheap, but there are better brands. If you want to go cheap, go cheap.
Another design is the following.
(2) GR Research SW-12B
http://www.gr-research.com/index.asp?PageAction=VIEWPROD&ProdID=131
3 cubic feet sealed
300 watt BASH plate subwoofer amplifier
It will hit down to 25 Hz and the cost is about $350 with out including shipping and handling. Also with out material cost. Max SPL is 105 dB. Do not forget to add some polyfill or acoustic foam.
Another configuration with the same woofers as above, but a ported or bass reflex.
4.6 cubic feet
Tuned between 20 Hz to 25 Hz
500 watt BASH plate subwoofer amplifier
It should handle down to 20 Hz with a lot of ease even though it is being slightly over powered. The ports should be at least two 4 inch ports with a straight length between 32.677 inches (about 20 Hz) to 20.078 inches (about 25 Hz).
Yes, you can build a subwoofer and have it working right. Subwoofers are the easiest compared to building a multi-way loudspeaker. Subwoofer design can go crazy if the mind wonders. A sealed type for subwoofers are the easiest and they are 100% guarantee they will work that is close to what is predicted. Ported or bass reflex is a little harder because there is ports that have to be calculated and have to worry about Xmax. Passive radiators are a side step to making ported subwoofers, but they use a movable membrane to tune the box. A passive radiator can be another woofer with out a voice. The passive radiators are tuned with weights. Bandpass subwoofers is the hardest to build because a lot can go wrong like burn up the voice coil. Passive radiators can as hard as bandpass subwoofers when more than one passive radiator is used. Though there are exotic types like transmission line and horn loading, but the amount of simulations is slim to none.
Use wood screws, but do not use dry wall screws for subwoofers. The pressure inside a subwoofer box is a lot. Always drill pilot holes for MDF.