The stone is indispensable for a crisp crust IMO. With a screen or without, it's the heat source that cooks the bottom quickly and evenly.
A screen only eases handling. I don't believe it improves the crust. It's main function in a pizza shop is to allow the pie to slide easily off the peel into the oven. An skilled pizzaiolo knows how to flick an (unscreened) pizza off a floured peel, whereas a chain pizza operation runs through lots of kids who are more prone to make mistakes
Home cooks that don't own a peel will find it handy too, but it's no substitute for a stone.
I agree with the stone, I leave mine in the oven to help keep the heat even. I put a sprinkle of corn meal on my peel It seems to help the dough "roll" from peel to stone.
I've always used a screen for reheating precooked pies, or stopping the effect of the stone on the crust, while allowing the toppings and crust to continue browning. Its all a matter of how much char you want on your crust.
My method: Build your pie on a semolina dusted counter top, or on top of a well dusted peel. If you build it on the counter, get ready to learn the art of gentle dexterity, because inserting the peel under a pie is difficult. Remember that the pie can be coaxed back into roundness and the toppings redistributed if you have a near disaster. Metal is easier than a fat wood peel, but both are possible given the right amount of semolina, dough consistancy, thickness of toppings, and good luck. Slide onto a well heated stone. Once the pie has fully set insert the screen to stop the crust from charring. Use the screen to reheat slices.
re: Karl Gerstenberger
Better yet is to use a wooden peel for putting a pizza in the oven and a metal one for turning (if necessary) and taking it out. Wood holds the flour and/or cornmeal a bit so that the dough can be placed on it and will not stick. It's harder to spread flour and meal on a metal peel. But metal is thinner and slides easily under a cooked pie.
Why would you want to stop the crust from charring?
A tile works fine if it's big enough and not outgassing anything nasty.
Come to think of it, all the pizza "stones" I've owned have been tiles. I've had several terracotta ones break. The current one seems to be made out of tougher stuff--some kind of porcelain? Looks sort of like the lining of a kiln.
re: Robert Lauriston
Charring aka "black stuff" is sometimes unpopular with the same crowd that generally doesn't like "green stuff" (bratty kids). Bring the char on I say! Others think anything black is burned and you can go deep gold and crisp with a screen.
Floor tiles, slabs of concrete etc. in addition to having unknown coatings etc. also don't have the ability to take high heat that a pizza stone does. Even so pizza stones will sometimes crack if they're placed in a hot oven - they need to be preheated along with the oven.
Professor Salt implied but did not explicitly mention that the stone retains a large amount of heat. Most ovens cycle on and off during the cooking process...by preheating a stone, one gets constant, even heating providing maximally yumminess and a GBD crust!
I spin the dough out and lay it on the screen. An inital drizzle of olive oil and then it goes into the oven (I set the screen right on top of the stone). Bake about five minutes, just to get a nice amount of oven spring on the crust and to firm the bottom up. Pop any large bubbles that form.
Then I pull the dough and the screen out and set it on the counter. Sauce and cheese and whatever else goes on at this point. I slide my (dry!) peel between the screen and the pizza, lift the pizza up and set it back in the oven directly on the stone. If I think about it, I sprinkle a tablespoon or so of fine cornmeal or semolina flour on the stone right before the pizza goes on it.
1. Because the dough is already set up enough to be soild, I don't have to worry about it sticking to the peel as I slide it on the stone.
2. The crust gets a little bit of a head start so that it will be brown around the edges around the same time that the cheese melts and begins to blister the way I like it.
3. The little bit of texture that the screen imprints on the bottom of the crust helps it stand off the stone a little and makes for easier removal later. This is not so much of an issue if one uses the cornmeal or semolina.
When I do pizzas on the charcoal grill, I actually leave the pizza on the screen for the whole cooking process, because the stone gets super super hot (650 degrees?) and I need that little buffer of space, otherwise the bottom is black before the cheese melts.
BONUS ROUND! Pizza screens are terrific for baking french fries on, because the hot air can circulate up and around each individual piece.
Here's what I use instead of a stone. It's heavy, but it works great to get a crispy bottomed crust - Lodge Preseasoned Cast iron pizza pan.
It has a handle on each side for easy handling in and out of the oven. I sometimes preheat the pan in the oven before I put the dough on, but not always. If you do, you gotta be careful to not burn your fingers. I do always proof my naked crusts for a few minutes before I put my toppings on.
With this pan my crusts are always crisp. After I take my pie out of the oven I usually let it set on the pan a few more minutes which makes it even more crispy.
I usually bake my pies at 500 degrees F, so the pizzas cook quick, though. I find this pan greatly superior to the stone pizza pan I used to use!
Building a pizza on a floured (or corn meal covered) baking sheet will allow you to slide it into a pizza stone, and you don't have to find a place to store a clumsy pizza peel.
I have used a piece of parchment paper in a pinch. Isn't easy to get a topping covered pizza into a hot over, but it can be done and baking a pizza on a smoking hot stone makes all the difference in the taste.
I build my pizza directly on the oven peel (metal) which has been dusted with cornmeal. It slides off easily directly onto the baking stone. I use a baking stone recommended to me by someone who helped build one of the largest pizza chains in this country. It's called "Fibrament" and can be ordered from http://www.bakingstone.com/. It's available in round, rectangular or custom sizes. I bought a standard sized rectangular stone that fits my oven perfectly. and leave it in the oven all the time. It does a wonderful job baking bread. You can also order flour specifically formulated for pizza from the King Arthur Flour Company at http://www.bakerscatalogue.com. It will give you a crust that is crispy on the outside and chewy inside. Hope you find this helpful.