Hi, Anthony... and welcome!
I have used parchment in the past, and, if my dough is really wet and I think there might be a problem, I still do. I use it in my kitchen oven set at 550o F and have never had a problem with it catching fire even though regular paper combusts at 451o F. What I usually do is cut off the big corners, slide the pizza with parchment onto the stone and wait a minute or two. Then, when the crust has set a bit, I reach in with tongs or my fingers and jerk the parchment out from under the pizza so that it can cook directly on the stone for most of the baking time and crisp up properly. This method works very well, at least for me.
I don't know your skill level with the peel and stone, but as you gain some more experience, it may get easier. I have also found that rice flour works VERY well to "grease" the peel... moreso than regular flour, cornmeal or semolina and doesn't give any burned flavors to the bottom of the crust. Bob's Red Mill sells rice flour... their products may even be in your grocery store, depending on where you live.
Hope that helps!