I built a 19 gallon system for a buildoff contest. Constructed the tank, the stand, the skimmer, modified a 10 gallon tank into a sump/refugium, built canopy and retrofitted a 2-36W PC and 175W MH light, bought a little rock, but had most of it. Got frags from my main tank, but also bought a $100 worth of frags. Cost? Nearly $600.
Can it be done cheaper? Yes. I could have made the stand out of pine instead of hardwood.
Lighting. If I'd decided to go softies instead of sps I wouldn't have needed a
metal halide light (though over the long run a metal halide (MH) is cheaper to operate)
Frag corals or gimmees from friends instead of dropping $100
Maybe $400 total cost
Could I have done it more expensively?
Oh Lord yes. Buy a skimmer, buy a tank(custom and starfire glass), stand and canopy with lights. Buy all your corals (expensive ones like Acans, A. tortuosa, Micromussa) you could end up spending thousands.