Its completely possible to do a reef in a 20 gallon tank. I have one in a 3 gallon! filter floss is that blue and white filter stuff that comes in sheets and you usually cut into the size you need.
Poly Value Pack
No need for a sump for anything under 50 gallons. Just keep up with 10-20% water changes a week. That is all that is needed.
For lighting, maybe Current USA Nova Extreme SLR. I think you would want the 30 inch saltwater version, possibly the 36 inch (there may be some hang over the sides, but not really an issue, better coverage IMO
). I've used the Nova Extreme series from the SLR to the Pro's. They make really nice T5HO fixtures.
Aquarium Lighting for Freshwater and Reef Systems: Nova Extreme Compact SLR T-5 Fixtures