Well, to be honest, it's going to be hard to sum up and entire cost for you being that a lot of things cost different prices, and sometimes you can get them used for cheaper, and sometimes you can't. I would say however, that in your situation, the lighting will be the most expensive, as always in SW when you are buying lights. Since you're not using a very big tank, whether or not you go with a 20G or a 10G, you will not need a protein skimmer. Simple water changes will achieve the same goal in this case. You will want to have some form of filtration though, so either you can get live rock, which will provide biological filtration, or you can get a HOB filter, which will provide mechanical filtration. Different methods, same results. And you could always do both haha. I personally would go with the live rock. Also, you will need a decent heater for the tank. Generally a good heater for a 10G tank would cost up to 20$, but for a 20G you can assume it would be maybe in the 25-30$ range. If it were me personally, i would save up some extra money and just go with the 20G. You can fit more in there, and it will give you more leniency on the water parameters, versus a 10G. In a reef tank, you want as little water fluctuations as possible, and really that goes for any tank, so having more water volume will give you margin for error. And for the live rock, generally you can go with 1.5-2lbs per gallon, but if your on a budget, i would say that 1lb per gallon could get you by.
You should also start thinking about what you want to have in that tank, as far as livestock goes. It's always best to plan ahead, so you can buy equipment accordingly. For the lights, in this case, i would say to go with PC lighting, since the tanks your thinking of aren't very large, nor deep. So PC lighting would be a good choice for you, and also a good choice to save money, considering they are not as expensive as T5 lights or metal halide lights. And for fish, i would say go with clowns, some gobies, some blennies, and firefish. Those are all great choices when dealing with tanks as small as those.
Buying frags instead of full grown coral is always a great way to save some money, and sometimes you can get them free, or for the price of shipping, if someone is giving them out. Just remember that coral grow, so even if you have a frag, it will become a fully grown coral someday!
Now here's something else to think about. You may want to consider just saving up the money, and then paying up front and getting a BioCube. Only because it comes with everything you need, to instantly start your SW tank. It may even cost you less money in the long haul as far as equipment goes. And you could get something like the 8G or 14G since they aren't that expensive. Just think, that with all the things you have to buy, you could have saved a little bit of money by just buying a kit with everything needed included. Just something to think about. I mean, if you plan ahead, and you know you can setup your tank for less than one of those BioCubes, then by all means, just go your route.
Anyways, come back here for more answers to your questions, and im excited since you starting a SW! You're going to love it. It's a lot of fun.
Good Luck!
