There is something that is "off" about your intro to your question: "When your seeds germinate, and reach an adequate height to go under lights…"
You should be putting them under light as soon as they sprout. They need light and lots of it.
Also, if you immediately put a fan on them, you won't have to go through a gradual process to get them used to the "wind", which will make bringing them outdoors all the easier in the spring.
Think about plants that start outdoors without any human interference - the plant drops a seed and that seed germinates and grows in full sunlight and full wind - 24 hours worth of wind. Whatever conditions you can create indoors to simulate that, the better as you're going to ultimately take them outdoors.
Transferring into starter mix or potting soil…. Most packaged potting soils have fertilizer built in, and that fertilizer is often too strong for seedlings (heck, sometimes the company that makes it messes up and puts in too much fertilizer for about any plant.) Ideally you'll keep them in starter soil until several sets of true leaves form. Alternately, mix a little bit of potting soil into your starter soil.