You do not need any sort of mechanical filtration at all. The live rock will be your primary filtration system in the tank. It will process most waste for you. Therefore, no need to buy any filter.
He meant "LFS" which stands for Local Fish Store. I tend to disagree with buying premixed water from the LFS, though, unless you know exactly how it is mixed or where it comes from. Mixing your own water allows you to precisely control the contents and makes me personally feel a little better.
A good protein skimmer is a fantastic addition to any SW tank in my opinion, but it is not necessary. Many people have ran successful reef aquariums without a skimmer....but skimming does make things easier for us and allows us to feed a little more regularly and gives a little bit extra room for minor mistakes in my opinion.
Most people highly recommend the Reef Octopus skimmers. Get one that is rated for a few times your tank volume. Since you don't have a sump you'll want to look for a hang-on-back (or "HOB") style skimmer. This is what I have (I have an AquaC Remora).
As for lights...there are MANY options. If you hope to keep corals, you will need powerful lighting. Depending on the dimensions of your tank, this is likely to be the biggest investment.
There are three main types of reef lighting:
1. Metal Halide is a tried and true way to light a reef tank. Many people like the colors of their corals under MH lighting. The drawbacks, though, are that the bulbs don't last that long, the power consumption (and associated costs) are high, and they produce a significant amount of heat (enough to raise the temperature in the tank, which isn't optimal).
2. T5 or VHO bulbs. This is probably the cheapest option of the three. Many people go with this option because of the costs, but you'll need to find a quality fixture and then purchase some quality bulbs....which have to be replaced (I believe around once every 6-8 months) fairly often. These get hot but not nearly as hot as MH lights.
3. LEDs are the new wave of reef lighting. The technology remains in a middle state (was in its infancy a couple years ago), but it is promising. I use LEDs on my tank. It is the most expensive option typically, but that initial investment is usually realized over time when you consider that the LEDs have at least 50,000 hours of life, consume very little power and do not produce a lot of heat. They're also available in many different wavelengths, can sometimes be programmed with cool effects like cloud cover and storms, etc.
Some quality LEDs would be the AI Sol, EcoTech Marine Radions, Kessil A350w.
Alternatively, if you are so inclined, you can build your own LED lighting fixture. There are many guides on this and other sites to do this and it is the most cost-effective way of doing it.
Your first step in setting up this tank should be RESEARCH. Make sure you read the guides on here about cycling your tank (and don't skip steps.....it will end up costing you. Guaranteed.). Research as much information as you can and keep asking questions. :) Good luck!
