The tomatoes I don't manage to eat fresh, I wipe clean with a damp cloth and put in the freezer in a cardboard box. When my box is full, it's sauce time or soup time or ... . Or I bag them up for fresh tomato soup in the middle of the winter. If the tomatoes are frozen, the peel comes off under cold water. I don't normally worry about the core as my biggest tomatoes are only 4 oz or so.
Daisy