They top will hold in the humidity just like a greenhouse. Fold in the bottom and secure it with a strip of masking tape, and the container can plant right into the garden and disintegrate. The great thing is you can customize both the height and the depth of the container by using different size newspaper strips and different size molds. Plastic Margarine Tubs with holes poked in the bottom for drainage. Use them for seeds and cuttings.
Cups Use paper or styrofoam cups.
Just poke a hole in the bottom for drainage. Also old pie tins, or foil pans are good to use. For a budget heat mat, you can buy a plumbing heat tape, a mortar tub, and a couple of bags of sand at the local hardware store. Put the heat tape in the bottom of the tub, cover it with sand, place your containers on the sand, and your seeds will have a toasty warm environment in which to germinate. Those giant sweater boxes with the clear tops that you can find at some discount stores make great containers for the sand, too, and they have a clear top to hold in the moisture and let in the light.