I only use regular potting soil, not seed starting soil. These days I make my own, but for years I just used regular Miracle Gro potting soil. You have to be careful, you don't want the moisture control kind, stays too wet. It has M-G fertilizer in it, which the seeds and baby seedlings don't need, but it doesn't hurt them. They do fine in it. Since it has M-G built in you don't need to add any other fertilizer for a good while.
You mentioned the coconut coir bricks. In making my own potting/ seed starting mix, I use those, but only as one ingredient, with mushroom compost and rice hulls (most people would use perlite). I don't like using a sterile seed starting mix. The little seedlings start needing some nutrients very soon after sprouting and then what do you do? Too soon to transplant, so you have to try fertilizing babies, which is easy to over-do with added ferts.