I "germinate" in nutrient solution. Tomatoes are heavy eaters and you almost can't overfeed them.

I transplant seedlings when the top plant is anywhere from 4" to 8" tall. If you have been growing them in good nutrient, the roots should be fairly short and pure white. If you've let them rely on their stored nutrient (from the seed), the roots are likely to be long and lanky -- not good!

I grow tomatoes at 2.5 EC. You'll need a quality EC measuring device to check and maintain it. I (of late) use a Bluelab Truncheon.