Determinate or Indeterminate
Determinate varieties tend to be more bush-like, and they will generally grow to a set height. They bear fruit over a narrow window of time. Indeterminate varieties are more vine-like, and they will grow throughout the season with a continual production of fruit. For the home gardener, I would recommend an indeterminate variety, but they will generally require more support, which we will cover under a separate topic.
Heirloom or Hybrid
Heirloom tomatoes are unique in that you can save the seeds, plant them next year, and they will produce the same type of tomato year after year. Some claim them to be more flavorful as well. The downside is they tend to be less disease resistant. Hybrid tomatoes are created by cross-pollination of two plants to produce a plant/fruit with the best characteristics of each parent. This usually improves the disease resistance, but the drawback is that re-using the seeds will provide a plant with unreliable features. If you are going to use hybrids, you will need to buy new seeds every year.
There are hundreds of varieties. You will need to determine the size you want, which can range from the size of a grape to fruits the size of a softball. There are also many colors beyond the typical red tomato – yellow, orange, green, purple, brown, and almost black varieties. The problem with choosing the best tomato for you is understanding what works in your soil type and climate. The best recommendation I can make is to consult your county extension agent for advice.
I live in central Georgia, where the summers are hot and humid. Our soil also contains a lot of clay. The variety that works best for me is Better Boy. I experiment with other types every year, but I use Better Boys as my main crop. It produces a large crop of medium-large tomatoes with an excellent taste.