Teal,
For a first tank, I suggest getting easy stuff to care for like mushroom corals and button polyps. You could get away without using super intense lighting, maybe just a couple of 13 watt power compact bulbs (I like the look of one 10000K and one actinic bulb). Put a layer of very fine sand on the bottom, some live rock on top of that, and you have a tank. Filters with sponges, bioballs and such are completely unnecessary in marine tanks (unless you're reading a book that's 20 years old), so all you need to add are something to move and heat the water--powerheads and a heater. You could probably go with two small powerheads like maxijet 400s and any small heater.
A protein skimmer is, in my opinion, optional on such a small tank, but adding one will definitely help. The BakPak from CPR is an excellent skimmer for a tank that size.
Keeping soft corals only would negate the need for calcium addition. Although soft corals use a bit of it, regular weekly water changes (around 5-10%) will be enough to replenish the calcium and other elements they use. One of the things that kept me from keeping stony corals for so long was the daunting talk of calcium reactors, kalkwasser, carbonate hardness, alkalinity, etc. I suggest learning how to keep easy corals first, then worry about the hard stuff. Stony corals really shouldn't be kept in a first tank, in my opinion. If you do decide to use calcium, however,
B-Ionic from
ESV is another quality product.
For fish, you have tons of options. I don't really think some clowns belong in a tank that small (maroons and tom
atoes to name a couple), but ocellaris clowns (Nemos) would probably do OK. Pairs are easy to find or make, and clowns are incredibly hardy fish. I don't think you should have more than two full grown clown sized fish in that size tank. A royal gramma, firefish, smaller dottyback, goby, sixline wrasse, or caribbean pygmy angel would all do OK. If I had a 10g I'd add a pair of orchid dottybacks, but that's just me.