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.
I prefer to used cardboard milk cartons, but also use plastic milk jugs. Now make a lid from the second carton by cutting around the box about 60 mm above the bottom. Turn this lid upside down and let it telescope over the box made from the first carton. Wash the carton immediately after emptying the milk. Using Plastic Milk Jugs Make a box from 2 plastic milk jugs about the same as above.