I'm fairly new at this too but I can answer most of your questions. Live rock is rock that has recently been in the ocean and has various organisms such as coralline algae, sponges, corals, and macro algaes growing on it. It also has a host of beneficial bacteria living deep within the rock. This is probably the most important quality of live rock. These bacteria form the most important part of your biological filter in your tank. And because of all this life, live rock has to be kept in tanks when in the fish store. When you receive it you usually have to cure it, a very important process to allow the natural die off to complete and the ammonia and nitrate levels to dissipate. Base rock can be virtually any kind of rock, from the ocean or terrestrial. The base rock sold in stores is usually oceanic, which means it is usually derived of some kind of coral. This rock will be just like the live rock except it has no life on it. It is dry and barren. It also can be more square or flattened. It is a lot cheaper than live rock so some people use it to form the base of the reef, then add live rock on top. In time, the base rock will become live also. You can also get terrestrial rock from a building supply store for much cheaper. Just make sure the kind you choose won't leach harmful chemicals into the water. Also make sure it is a porous rock so that the bacteria can colonize deep inside it.
You do NOT need an overflow when not using a sump or refugium. The simplest way to go with your tank is to get a good protein skimmer and a lot of live rock and live sand. If you are trying to save money you can get some base rock and regular sand and seed it with live rock and live sand. In time it will all become alive. In this setup you have everything contained in your main tank, so you don't need an overflow or any external plumbing.
Small pieces of coral occasionally come on live rock, but usually it is all dead by the time it gets to you. You can purchase corals, either attatched to rocks, in which case you just put the rock into your tank, or as a single polyp, when you would attach it to a rock in your tank. Either way they will eventually spread onto the other rocks in your tank.
The reef is just a general term for the whole structure. You can build a reef out of just rock. Or you can add corals and collectively it is termed the reef.
The best advice I can give you, as one beginner to another, is to research AS MUCH AS YOU CAN before you buy. I spent probably 5 or 6 months just reading about reef tanks before buying anything (because I couldn't afford anything, but it was for the best). And it's not like I was starting completely from scratch. I have had FW tanks my whole life, and I am a senior marine biology student, so I already had a fair amount of knowledge. Learning everything beforehand will save you a lot of trouble, wasted effort, and money. If you can, go to a bookstore and look through all their books on reefs, and buy one or two that are really good. They will detail everything from tanks to filtration setups to lighting to fish to diseases and maintenance. The book I got describes about 5 different filtration styles and setups, and even tells you how to set up a tank from scratch. There is just so much to know in this hobby you need a source to be able to reference at any time. I hope this helps, and don't be afraid to keep asking questions.
