A tank of some sort, the larger the better (to a point). I would think that 55 to 200 gallons would be ideal for a beginner, depending on space, time, money and what you want in the end. Remember that the larger it is the more the accessories will cost (lighting, skimmers, etc.). Also, the more stable of an environment it will provide I have heard of mini reefs as small as 1 gallon though. I would however leave these to those that have a little more experience. That might be a cool project for when we have more experience (I am talking a couple of years).
Some sort of filtration.
A sump. I am sure that there is some discussion as to whether or not it is really NEEDED, but I believe that it is a must. It is a great place to put a skimmer, your heater, chemical filtration if and when needed, testing probes, a tank ground, a good place to dose or add makeup water, and it increases the total volume of your tank by however much you want (depending on the size you can cram down there, in theory you could have a 1000 gallon holding tank/sump that circulated water into a 55 gallon viewing tank that would be very stable, this is extreme, but you know what I mean). You can purchase something specifically for this, use a smaller tank (10 or 20 or whatever you want) or use a Rubbermaid bucket that is the right size for you. Try to get a light colored plastic bucket if you can. there are reports of some plastics leaching some chemicals into the water that they contain.
Some kind of stand. I tried to skimp here and ended up tearing down the tank to put a real stand under it. Remember that salt water weighs around eight and a half pounds per gallon. Also consider any sand bed, rocks, and other ornamentals. I think that I read that a 55 gallon reef tank can weigh around 800 pounds, make sure that the floor can take the weight of the aquarium that you are going to put there as well. Make sure that the skimmer that you want to put in the tank will fit into the stand if you are putting a sump in it and are going to run a skimmer in the sump. That means that you have to decide all of this before purchasing anything.
A thin foam pad of some sort to put between the tank and the stand. This will help the tank distribute its weight evenly to the stand. This can be very important, as you don't want to cause the tank to warp in any direction except what it is designed to. This can lead to stress in the seams and the eventual leak.
A heater, I think that you can't skimp on this one, as they are cheap in relation to everything else. You want around 3 watts per gallon of water that needs to be heated (the total capacity of your tank, including sump). You may also want to pick up a 25 watt heater just in case you have to make a holding tank out of a plastic bucket overnight in an emergency. You should have an extra heater for the main tank! Remember that glass tanks will need more wattage than acrylic tanks. This has to do with the insulating properties of both materials. It is generally considered a good idea to have two heaters that are each half the total wattage that you will need. this will help if one of the heaters sticks in the "on" position.
Test kits, You will need at the minimum, Ammonia , Nitrite, Nitrate, pH, and Alkalinity. You may also want (and will need at some point anyway) Calcium, copper, Phosphate, chlorine and chloramine. You will also have to have a salinity tester.
Nets, I suggest a few of different sizes, this helps when you HAVE to catch something (you should, however, try to abstain from catching anything unless absolutely necessary, as it causes stress).
A large container for mixing salt water (you can use a Rubbermaid garbage can, if you like, but remember to get a light colored one and keep away from the green).
A couple of 5 gallon plastic buckets (yes, you will need them for something).
Powerheads for water circulation within the tank. I run 1 MJ 1000 and one MJ400 in my 55 tall with a Rio 1700 as the sump return and get pretty good circulation. You want to try for water movement in all areas of the tank (i.e. no dead spots). .
A couple of extra powerheads, I have a couple extra of the ones that I use in my tank for water circulation. That way if I need to move or mix water, it is a lot easier to do. Also, if a powerhead burns out, I can just replace it. Of course, this also means that you will need tubing that fits on the powerheads that you use. I have a window pretty close to my tank, so I just run the tubing from the tank to the outdoors, hook it to a powerhead till the tube fills with water, then let gravity take care of the rest for my water changes (I refill in the same manner, I have an identical powerhead running in my new saltwater to mix and aerate it, so I just leave the tube in the tank and hook it to the powerhead in the new saltwater container).
Several thermometers, one in your main tank, and one for your makeup water, and another just in case (say that you have to put some of your inhabitants in a 5 gallon plastic bucket for some reason or another, you will have to maintain the temperature in that bucket). You should always have an extra on hand of anything that is imperative to the tank running (heater, sump pump, etc. as it will only go dead 5 minutes after the fish store closes and when the next day is a holiday :0.
A spreadsheet application on your computer, aquarium software, or a notebook to make notes on your tank. You should keep records as to what is happening in the tank. You should date and keep track of all of the tests that you take, and you should note water changes and the amount with the date as well. I also note what creatures that I have added and the date. This way if something goes wrong, you can refer back to your notes and see if something correlates to the beginning of the problem. I note everything, including dosing supplements and vitamins (how much and what date). It is also a good idea to have logged the Latin name of all of your animals. that way if you have a question you can get help quicker.
Various plastic measuring cups and spoons for mixing salt water and for dosing the tank (you will not really be dosing until you finish cycling though).