So...by suckers do you mean any branches coming off the main stem?
Sorry to sound like a newb, but I've only ever had a hobby garden, no formal training by anyone on care of vegetable plants. We always let the plant grow as is and whatever we harvested is what we got. This year I noticed that I had a lot of small tomatoes and I'm interested in learning the right techniques to get fewer but larger fruits.
The plant will have 1 main trunk coming out of the ground, prune the first 4 lowest shoots off. There needs to be main branching off the trunk to provide shade. You need to leave the big main branching, but you'll see a sucker growing out of the crotch or Y where the main branches come off the trunk. Every one of these suckers will flower and make a mess of small tomatoes. It's the suckers coming out of the Y that need to be pruned. There are 2 types off tomatoes, indeterminate and determinate. The indeterminate will keep growing till a frost. The determinate type form more of a bush that lay on the ground, low and compact. If the plants are allowed to lay on the ground, you'll get a lot of rot, that's why a use a trellis, but those wire baskets aren't bad, but heavy producers like Goliath will really fill up a wire basket. You got to keep them off the ground. Going back to the first lower pruning, after you get rid of the first 4, let the plant grow for a couple weeks before you start more pruning. If you want more info, I'll be glad to help. I like growing tomatoes !!