Seed starting mix for the very initial germination is usually sterile. The seeds have everything the seedling needs for life, so there's no need for any nutrients. Using sterilized seed starter at first will help avoid damping off disease which can cause the stems to fall over.
Shortly after that phase you need to up-pot and the plant will need macro nutrients. If you use the Miracle Gro, commercial product their instructions expect you to keep adding more and more of their chemical fertilizer. This is a lot of work and, in my opinion, somewhat expensive. If you up-pot before planting out, I would seek out a potting soil with some good long-release macro-nutrient sources and composted organic matter.
Potting mix will work well enough to start seedlings in general, though. I wouldn't worry too hard about it, especially for tomatoes. You should always bury the tomato stem deep as you plant it outside which will mitigate damping off. Expect that some of the seeds won't germinate and some of them won't transplant outside, so if you want to have 10 plants in the end, start with ~20 seeds.
Most seeds do not need light at first, but they will need it as soon as their first leaves sprout. Seeds do prefer warmer temperatures, and a light placed close to the soil can help them achieve that warmth.