When I'm doing a bunch of pies they all go on parchment. The parchment burns somewhere above 500F so only leave it on for a minute or two, then I pull it and rotate the pizza a quarter turn. I trim the parchment with scissors to a 1/4 to 1/2 inch from the edge, except for a small tab to help pull it out.
Some in my family don't like the cornmeal on the crust so the parchment takes that out of play.
For me, I don't mind cornmeal and if its my pie, it is usually the last pie of the night so while I'm topping the pie the stone is recovering heat and I go without parchment and use cornmeal. I don't know if it makes a difference or not on the crispiness, but I like it this way.
I'd use semolina but that's hard to find right now.