I'll second Tooge and suggest Brandywine. I've always had excellent results with them - huge, meaty fruit with the soft flesh you are talking about. Bumper crops. I usually end up with more Brandywine than anything else.
For the second variety, I'd suggest Old German. Smaller sized fruit, but soft, sweet and succulent. You've got to watch them carefully as they ripen because they get there really quickly, but you'll be very pleased with the results.
If you want to go the opposite direction, Green Zebras are fantastic. Maybe the best tasting tomato out there, but they are thick skinned and a little tough.
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