Welcome to Captive Reefing!! and to an obsession that can last a lifetime. This forum is here for those who are new to reef keeping to ask questions and receive guidance from the membership here.
First and foremost you will need to select and aquarium that will meet the needs of the animals that you intend to keep. Pay close attention to this first but very fundamental step. Tanks come in many different shapes and sizes. I would recommend something either square or rectangular as a first tank. The odd shapes like hexagons and triangular tanks are interesting to look at but present challenges where lighting and flow are concerned. For the first time out stick with something that is pretty standard
There are some neat options now in the realm of nano reefing where the tanks filtration and lighting are all integrated into the tank itself. I am not sure I would recommend the smaller versions of this type of set up but I believe they are available in a 29 gallon version. Nano reefs present a different set of challenges that someone more versed in keeping a small system will be able to answer. It is typically easier to control variables like temperature for instance in a larger volume of water than it is in a smaller volume of water.
During the tank selection it is important to have an idea of what your goals are for the tank. Do you want to keep just fish with a few inverts like cleaner shrimp? What type of fish are you interested in? Will the aquarium provide enough territory and space for them to grow? Will the fish you're interested in be compatible with one another or the other animals that the tank may house (corals and inverts)? It is important to consider all of this while in the planning phase before you ever spend a dime on a tank spend a few dollars on a good reference. Reading is underrated and a lot can still be learned by picking up a book. This will ensure that you're making an informed decision rather than taking someone elses word as the gospel of reef keeping.
Once you select the tank then the fun really starts!!! Some basic equipment would be a protein skimmer, lighting, heater, circulation pumps, test kits, salt, and a sump (optional but in my book it is essential).
Protein skimmers are essential IMO because they are constantly removing organics from the water while at the same time increasing the amount of oxygen in the water. A good skimmer is worth its weight in gold. There are as many skimmers on the market today as there are car models on a lot. My advice on this topic is to ask other reefers for suggestions until you get a good handle on the hobby and which manufacturers have good reputations. I always go a little bigger than what I need too because the ratings on skimmers can be questionalbe based on the stocking levels of the test tanks vs "real world" tanks.
A protein skimmer works by mixing air and water in a venturi set up. As the air is drawn in it is "chopped" into fine bubbles by the skimmers pump. This fine air carries protein and other organic matter put of the water and into a collection cup to be disgarded. It is analogous to the sea foam prduced by waves breaking near the shore only we are doing it in a container
Lighting is as controversial a subject among reefers as what came first, the chicken or the egg. A common misconception amoung new reefers has to do with watts. There is no stead fast way to say that X watts per gallon is the magic bullet. Simply put the qulaity of the lighting you use is as important if not more important than the amount of watts you have over a tank. A 100 watt incandescent light bulb will not put out the same amount of light as a 54 watt T5 HO flourescent bulb will. That incandescent light also will not provide the spectrum of light needed for corals to flourish in your tank.
A better way to approach this come down to what you're keeping in this tank of yours and waht your preference is. I am biased towards Metal Halide lights because they are intense and are a point source light. This means that they give shimmer lines much like when sunlight refracts in a swimming pool. I love that look and the results I get with them.
Others like the T5 HO bulbs and not without good reason. They allow for more manipulation of the overall look of the tank as many bulbs of different color temps may be combined. They are also just as effective at keeping high light demanding animals as Metal Halides.
Another area in lighting that has really taken off is the area of reflectors. There are some great choices for both type of lights that will really add bang for the buck when it comes to delivering the light where you want it - in the tank and not on your walls and ceiling! Lighitng is an area where it is advisable to do a lot of research because it is one of the biggest investments after a good skimmer!!!