I think the best thing you could do for a tank this size would be a refugium, maybe a 10 gallon tank, and a hang-on skimmer. My old 10 gal nano had a set up like that. It's really important to increase the water volume and have a place to grow macro algae and beneficial sand/rock animals. The skimmer will dramatically improve your water quality and keep O2 at saturation, which is very important for such a small tank.

This does not have to be expensive. The hardest part is drilling your 20 tall, or finding a decent hang on overflow that will fit. Other than that, you're looking at $10 for the 10 gal tank, maybe $25 or so for a used prizm or similiar hang on skimmer, which you could easily hang on the 10 gallon refugium, and $30 or so for a mag 5 to circulate water between the two (It won't be too much flow, believe me) and then scrounge for some sort of light over the refugium.

Reef tanks don't usually work well with mechanical filters or biowheels, which are really nothing more than tiny wet dry filters. Better to use the aragonite sand and live rock in your tank for bio-filtration, a skimmer for nutrient export and O2/ph issues, and macroalgae to deal with the quick build up of nitrates and phosphates.