A 20 long would do the job of course bigger would be better though, your biggest expenses are going to be the live rock and a good filter, a heavy canister could easily provide enough flow, so spending a few extra bucks on your filter could cut the need for powerheads. Something in the neighborhood of an Ehiem 2215 would be perfect.. That'll run you about $110. The big buzzkill is the cost of live rock, but this being a mantis tank you'll benefit from having lots of small pieces for your little beast to build things with(the coolest thing mantis shrimp do IMHO), the cool thing about that is most LFS have a hard time selling off the small chunks of rock that come in with their shipments, and this rubble rock is usually available on the cheap if you ask around for it, expect to have minimally 15 pounds of rock and to pay around 8 bucks a pound for it, 20-25 pounds would be even better. If you're buying at an LFS and can't get anyone to make a deal with you, you're looking at 160 bucks for your rock. Liverock can be found cheaper on craigslist or ebay, generally 4 bucks a pound for cheap stuff, just be careful ordering rock online, lots of people will send you dead, dry rock or rape you on shipping.
Lighting can be as simple or ridiculous as you want to pay for, if you're wanting to do corals or an anemone (condy+mantis tanks are a whole new kind of awesome) I'd spring for a dual HO T5 that you can retrofit into a cheap hood, total DIY cost would be about 80 bucks. I would shy away from any more light than that, halides have been shown to have degenerative effects on stomatopod exoskeletons, and you don't want that... Plus the lamps that put out that kind of light are way overpriced and will cook a 20G in a small, poorly ventilated dorm room, again learned from experience. If you're not comfortable retrofitting your own lights Coralife makes a good 20" dual PCF fixture you can get new for about $130. If you're not worried about growing things, a 10 dollar florescent lamp from home depot set down on top of a glass top will do just fine.
Skimming isn't necessary. Keeping anything that would really benefit from a skimmer is just a bad idea in a 20g anyway.
The best advice I can give is just not to buy crappy gear, you'll want the good stuff and will buy it eventually, and you'll kick yourself for wasting the money you did on substandard kit.
