Welcome Jess!
I am new to saltwater myself, but have done a LOT of reading. My suggestion is to get a minimum 55 gallon tank to start with. The bigger your wallet can afford--the better. This is because a larger tank is more forgiving in terms of water quality for the beginner. Small tanks are harder to keep under control.
You will also need a stand for the tank and a place to put it. Make sure the floor can hold it. A 55 gallon tank filled with water and rock can weigh over 5-600 pounds!
As far as equipment, don't skimp on the cheap stuff if you don't have to. You will end up upgrading sooner rather than later anyway as the cheap stuff is, well---cheap.
If your goal is a reef tank, you will more than likely need a protein skimmer. Get the best one you can afford that will do its job.
A sump or refugium (even better) will be of great use as you can store the skimmer and other things below the tank.
You will need a heater. In fact, two is better than one in case one fails. You need to maintain tank temperature as much as possible. Again, go with a good brand. Titanium is best and has less chance of braking and killing the tank.
A thermometer. Try to stay away from any containing mercury as they may also brake and destroy your tank.
A powerhead or two to keep flow going in the tank. This is also a must have.
As far as filtration, I suggest using live rock and live sand. A natural biological filtration system. Live rock costs money, but its worth it and will benefit your tank immensely.
Lights are a very important part of a set up as well. There are many variations of lighting. You should read up on this as much as possible as the type of lighting you need depends on what you plan on keeping in the tank in the long run.
Keep in mind, this hobby takes a lot of time, money and patience. A typical beginner set up (55 gallon) will run you $1000 and up. And thats before anything exciting goes into it.
While you're waiting to purchase these things, read, read, read!! The more you know, the better. Don't rush into anything.
I hope you find this site as helpful as I have! There are a lot of experienced reefers here.