Congratulations on getting this far!
Yes, you want regular potting mix, not seed starting mix, once you move them into pots. When you transplant the tomatoes (but not the other stuff), bury them deeper than they were, up to the true leaves. Tomatoes have the interesting property of being able to root all along the stem when buried like that, so it gives them a better root system.
If your potting mix has fertilizer in it (most do), then you won't need to add any for awhile. Fish emulsion is mainly Nitrogen. It's good for a growing boost, and also has trace minerals/ micro nutrients. But for continued growth, flowering, fruiting, you want something more balanced or other things along with the fish emulsion. Some of us like organic potting mixes like Planet Natural, Dr. Earth, Epsoma. But the Miracle-Gro won't hurt your plants. The most negative effects of synthetic fertilizers like that are on the soil web of life when you are growing in the ground. Your potting mix doesn't have much of that anyway, so you might as well use the M-G.
Otherwise is just how purist you want to be and how much you care about using petroleum based products.