I would say minimum enclosure size for an adult male would be 3' X 3' X 2' deep (about 130 gallons if filled to the top, but you would only want it filled half way). Obviously juveniles and females can be kept in smaller enclosures.

With a tank that size, and an animal that dirty, the best filtration option is probably a sump or filter chamber rather than a self-contained unit. If you're building the enclosure yourself, it's easy to add a filter chamber by walling off one end or a corner of the enclosure; add a pump, plumbing, baffles, and filter media. You can find more detailed info about building such chambers on various aquarium forums.