Try cherry and grape tomatoes. I've grown cherry tomatoes for the past two years along with starting grape tomatoes this year and I've had much more success with them than larger varieties. I think they tend to be more disease resistant, more vigorous, more productive, and fruit matures more quickly.

Also try growing them in bags or raised beds where it's kept away from the ground where pests can get at them easier. Another thing you can do is cover the soil around them with straw mulch in order to reduce soil splash onto the plant when it's being watered--this can transmit diseases to the plant. Pick off all the bottom half foot of leaves or so on the plant when it's big enough too to reduce soil splash hitting leaves.