We used to have an aquarium with tetras. They're very easy to keep alive, but you need warm water and a slightly acidic pH. You should definitely have a thermometer and pH tester. We ended up just mainly buying different types of tetras for our tank. They come in lots of different colors and shapes. Once your sure your tank is set up well, you should always buy at least 3-4 of each variety because they're schooling fish.
We had the biggest problem getting our pH right. It was always way to basic. We finally resolved it by putting a piece of driftwood in the tank. I don't know why that fixes it, but it does. We had to do a lot of water changes during the first few weeks after we put it in, though, because it made the water look like tea.