They are available in glass and several kinds of plastic. Most people use 20 to 25 mL of medium in each petri dish. They are all called culture dishes. Most platic dishes are make of polystyrene and can't be autoclaved because they deform in the heat. Some plastic dishes can be autoclaved, but they are more expensive.
Most people autoclave glass dishes and medium separately.
When the medium is cooled to about 55 o C, they lift the lid of the dish enough to pour the the medium to the desired depth and lower the lid in place. If your dishes are autoclaveable, you may dispense the agar into the dish and then autoclave. Store your Sterile Items in a Dust-free Place. The air of every workplace contains dust which will blow into or fall into your sterile medium. Many laboratories have dust free cabinets for storing their sterile medium and equipment.