The key to being inexpensive for a reef tank is finding the right light. Personally, when it comes to small systems and lighting for corals people either lean towards a PAR 38 light, which I don't personally have much knowledge of, or the taotronics LED
panel (or similar panels that are made over in China). That is as cheap as they come and are extremely low maintenance when it comes to not needing to replace bulbs ever 6 months.
You'll want to get yourself some sand, any aggregate will do, and some rock, which can be base or macro rock to save yourself even more money. You will want 1 lbs per gallon in the system.
In small systems under 30 gallons you can easily skip a skimmer and save yourself money, as it is easy to do water changes to address parameter issues in such a small scale.
You just want to make sure you stock the tank with appropriate livestock, as people always try to toss a fish in that is way too big for a tank or throw a ton of fish into it thinking that saltwater can work like freshwater when it comes to number of fish, like a fish per gallon rule. Check out the nano section at liveaquaria.com to start gathering ideas. I personally would have a nano tank with a clown goby or something similar for a really cool little tank.
What else would you like to know?