I would do 2 tomatoes in a 4x4’ and then plant something else at the base. At 3 and 4 tomatoes they are going to start shading each other other and only the ones facing towards the sun will be productive.
Quantity goes down as size increases, if you want a steady supply of a lot of tomatoes go with a cherry or plum (2-4 oz). Hybrids will also likely be more productive due to being more disease resistant and adaptable.
For pruning, I am of the opinion its not worth all the effort just to get maybe 20% more - Id rather just plant one more tomato. Tomatoes started indoors and fertilized properly can very easily get 8-10" tall and 3-4’ wide by the end of the season.
I’ll link to the way I grow tomatoes below, but you can also google “rebar mesh tomato cages”. Basically you plant the tomatoes and plop a 24" wide and 5’ tall cage over it, securing it to the ground somehow. Then the only pruning / training you have to do is removing the leaves touching the soil when the plants get tall enough and redirecting the branches that try to escape back into the cage. I wouldn’t grow them any other way.