free air subs are designed to be run exactly how the name suggests - without a box, alot of cars come with an optional subwoofer, when they do though they are usually reffering to a free air sub sitting in the parcel tray eg. my dads el fairmont
look at it from a physics point of view, bass is created when large quantities of air are displaced at speed, now a free air sub will need to displace the total air in your car to create the same amount of bass as the little sub and box in your boot (an impossible task)
free air subs usually don't have the power ratings, the cone extension, or the build quality of a typical in box subs
overall go for an enclosed sub over a free air sub any day and you'll be happy
as for what type of enclosure to put it in this is very personal but a general idea is:
Sealed: it's your good all rounder you won't get as high a db rating on certain frequencies but you'll have a larger range of bass coming from the sub/s
Ported: can be very loud but is usually tuned to certain frequencies and outside of it's tuning the bass drops off (or becomes sloppy) very easily
Band Passed: much like ported very selectively tuned to certain frequencies and bass will fall away quicker outside the ranges, great for SPL though
more info on boxes and making boxes can be found
>here< i learnt alot of stuff from reading the tutorials on the site particulary "The Myth Of The Magic Box"