Welcome to the site!
As you will experience, many people have different opinions in this hobby. Some things work, some don't. That is why you should do all the research that you can and it will take a little bit to figure out what will work for you.
First of all, I congratulate you on your decision to get into the saltwater fish hobby. It's a very rewarding hobby with many, many years of patience, experience, and research, - as you will figure out soon enough.
It looks like you are on the right track! Let me try to help you fill in the gaps.
Tank - This corner type of tank isn't the most ideal tank for saltwater. The reason is that it is very difficult to get the flow set up correctly. However, since you don't want to buy another tank, and would like to save a little money - I will go ahead and say that it's fine! If you happen upon someone else who has a corner tank, pay attention to the pictures and see where their powerheads are placed. (if it looks like they have a succesfull tank.)
Stand - How tall is your stand and what is it made of? Most standard store bought "put together" stands won't hold up to moisture and saltwater for very long. So, since it is such a concern for you not to find your tank in your downtown neighbors apartment, I would highly suggest changing the stand from the MDF board/particle board to something way more solid. If you already have a solid wood stand, then no worries.
Light - Any light will do, as long as it's made for saltwater fish. A small LED system would be nice. Fish don't have to have any sort of light at all, but it's nice to have one. lol. A light that is designed for salt water fish will bring out the colors a lot better then a standard 65k daylight freshwater lamp.
Overflow box - I highly recommend getting an overflow box if your tank isn't drilled already. The overflow will allow you to use a sump. (yes, you can use a 10g sump.) I personally use an Eshopps PK Nano (rated for 200gph on my 20g tank) but you would be better off going with the 500 model. They are relatively cheap, and since you already have a 10g tank laying around - a sump seems right up your alley.
Sump - Your sump can be a 10g tank - you will have to baffle it with some glass and silicone. There are several designs that work really well, however, you will have to do a lot of research on this before you can start baffling it. The first thing that you have to do is figure out what in-sump protein skimmer you want to buy, because that will determine what the "footprint" of the skimmer is, and how big the "chamber" of your sump needs to be.
Protein skimmer - as said earlier - you should do a lot of research on this subject. I highly recommend, for your system, to choose a skimmer that is rated for double your aquarium volume. (about 75g) Although I have never used one, an ASM Mini G is said to be a great skimmer (rated for 75g) has a small footprint, and is relatively cost effective ($~120) There's also an SC65 cone skimmer which is also pretty good and has a small footprint for about ($80) (I'de go with the ASM though...) So, first, figure out what protein skimmer you are going to buy, then figure out it's foot print and then you can baffle your sump. On a side note - make sure that the protein skimmer isn't taller than the bottom of your stand, and that you can lift the cup off for cleaning.
Powerhead - Do not skimp at this point. There are other places that you can skimp, but this is not one of them. I really like Koralia powerheads and I have used them for years. But, by the time you buy a couple of Koralias and a wave maker unit etc. you have just spent as much money as you would have on an MP10. (~$240). A Vortech MP10 is an awesome little powerhead. (I'm buying one for my 20g nano) it has variable flow rates, programmable flow rates, storm surges, nutrient export modes, wave maker and undertow capabilities and they can work wirelessly with a controller/adapter. Also, by purchasing a much better powerhead initially, it will save you money from upgrading in the future (which I think was one of your priorities.) I bought a couple of koralias for my 20g nano, and I am so disappointed - I am moving on to an MP10, and saved my $80 on the other powerheads.
One MP10 is perfect for your size tank, and it will give you much better flow rates and control than a bunch of powerheads would in your tank. (Plus, Vortech powerheads are very low profile, and make a nice clean look in the tank.)
Live sand and live rock - Live sand is a myth. I don't believe in live sand, dry aragonite sand will be seeded by organisms from your live rock. One 30 pound bag of dry aragonite sand (~$20) is perfect for your size tank. Live rock is also something that can be semi-skimped on. May I suggest buying 10-15 pounds of live rock and match it in weight to dry base rock. You don't want more dry base than live if you can help it. The live rock will seed the base rock and it will also seed your sand with organisms, microflora and fauna. It will also provide the bacteria for the initial Nitrogen cycle to get started.
Test Kits - API brand basic test kits is all you need for a fish only tank. You'll only be testing your aquarium for ammonia and nitrite within the first month of your cycle anyway. Then all you would test for is nitrate maybe once a year unless you are having problems.
I'll be back on later today if you need any more help.
