>>154125A picture of your plant(s) would help. Especially what variety. Some tomatoes are vines (indeterminate) and others are more like short bushes (determinate).
With indeterminate varieties of tomatoes you essentially, need at least 2 leaves under the lowest set of tomatoes. Anything below that doesn't matter and can be removed if it shows signs of disease or yellowing. Leave the top 1 foot of the plant alone, but below that you may pinch off/snap off the new suckers that grow up from between the leave and the main stalk. Stake it and it'll grow and grow (usually up to 6-7 feet outside of greenhouses for a season and up to 70-90 feet in a greenhouse with 2+ years of growth).
Only pinch off the shoots by using a quick snapping motion. Grab the main stalk with one hand, place your thumb just under the side of the sucker. With the other hand hold the sucker near the base and quickly snap it towards you. Prevent skin from tearing and running down the main plant. Suckers should be about 2 inches long with you remove them. Smaller ones are just annoying to remove and larger ones can cause problems. Let the grow larger, if you want to break them off at around 6 inches long and use those to plant to make more tomato plants like in this image.
For determinate you don't pinch out and instead let it be all bushy and do your best to maneuver it around so you can access all the growing tomatoes.
