When choosing tomato varieties, keep in mind that the number of days to maturity stated on the packet is the number of days from transplanting. For the number of days to maturity from planting the seeds, add about 50 days. Also remember that the number is just an estimate - add time for cool weather, shady conditions or just plain bad luck. Anything under 65 days is generally considered early, but there are many varieties that will produce even earlier.
Determinate, or bush plants, are shorter and grow well in cages, but they tend to set fruit over four to six weeks. Indeterminate plants will grow and produce fruit indefinitely until they are killed by frost, but they tend to be pretty wild unless they are staked and pruned. Experiment with both; some determinates might provide an entire season of fruit if frost comes early.
Hybrid, open-pollinated, or heirloom? Heirlooms are only open-pollinated varieties that are more than 50 years old; while preserving genetic diversity is important, newer varieties are often more productive and disease resistant. Plant these kinds if you want to save the seeds for planting. Hybrids are often very productive and disease resistant, but don't save the seeds because the plants won't be at all like the parents.
If you're looking for a couple good varieties to start with, here are some early varieties that are consistently recommended by the experts:
Early Girl: Hybrid, available in determinate or indeterminate forms. 53 days. 5 0z. fruit, high yields, good flavour.
Celebrity: Hybrid, determinate. 72 days. 8 oz. fruit, disease and crack resistant, very productive and flavourful, sets fruit under most conditions.
Stupice: Open-pollinated, indeterminate. 52 days. 2 oz. fruit, productive and sets fruit in cool weather.
Oregon Spring: Open-pollinated, determinate. 58 days. 4-7 oz. fruit, good yields even in cool weather.
Champion: Hybrid, indeterminate. 62 days. 10 oz. fruit, high yields.
Sungold: Hybrid, indeterminate. 60 days. Vigourous, productive plants that perform well even in cool weather, produces orange cherry tomatoes with excellent, sweet flavour.
Sweet 100: Hybrid, indeterminate. 60 days. Large, very productive cherry tomato plants. Sweet Million and Supersweet 100 are versions of Sweet 100 with improved disease resistance.