I plant in both containers and the ground, depending on type. The big stuff (like cherry tomatoes) goes into the ground, some of the smaller I've been trying out in these cheap but giant 7 gallon plastic pots. I have to make sure the pots get shaded enough to keep the roots cooler, but it works well if I have stuff I want to try and protect long enough to get the last crops. (I have a really short season.)
16" pots will work, depending on depth. The two big problems are enough room (tomatoes have huge root systems) and making sure the pots don't get too hot and cook the roots on a warm day. Cooking the roots might never be a problem if you are in San Francisco proper...
Try to keep the roots as undisturbed as possible, every move stresses them more. That's why I start in the solo cups, less moving and I can slowly add dirt to the tomatoes and bury their stem as they get taller. The loss rate on tomato seedlings tends to be so low that I plant one cup of each variety (2-3 seeds) and prune out if I need to.
(And I agree, heat mats are great but stuff dries out FAST.)
