Emily, if you can find or buy some largish plastic tubs (like rubbermaid) and drill holes in the bottom and lower sides for drainage and air, you could fill with a lightweight soil mix like for square foot gardens with lots of vermiculite, to reduce the weight of the container. You could even fill the bottom with some shipping peanuts for extra drainage and to reduce the weight further. Then you could scatter some of your seeds in a polyculture of mustard types, salad greens, herbs like dill and parsley, a few beets, chard, kale, and a cabbage or broccoli, etc, you could likely harvest greens over the summer, especially if you buy some clear containers the same size to use as a mini-greenhouse to cover at night. or on cloudy days. Maybe use a stick to just prop the top open on cool but sunny days.
Or you could do something similar with recycled pots (like from large potted trees) but it is a bit harder to cover those, though still possible. Or if you can find some old 2x boards, of whatever size, you could nail them together and make a bed, then just take it apart and scatter the soil when you have to leave.
Don't try to use regular dirt in containers, it packs down and is too hard for the plant roots, so a mix of peat,
compost, and vermiculite seems to work better in container gardens.
Don't plant too thick, Toby Hemenway said about 1 seed every 2 inches is about right for a polyculture, then pull out plants to thin so they aren't too crowded. You can cut the bottom inch off green onions you buy and stick the bottom into your "planter" as well, and be able to snip off green leaves to use in stir-fries etc. I read that you can do that with celery, too, but mine haven't done much growing.