Hey man, yeah you can use the same soil all the way through. Potting soil with perlite or vermiculite added should suffice, in about a 4-1 ratio, and yeah stay away from the clay.

Transplanting can be a bit messy but is easy. Usually most people start seeds in party cups(with drainage holes), and once they are ~2 weeks old, usually they have enough roots to be transplanted. Like in the thread DP posted, you can see the rootball at the bottom of the dirt, all massed up. Thats a pretty good sign that its time to move em. When you go to transplant, just squeeze the pot a bit and turn upside down, and it should slide right out and into their new home.