I think to be honest you will struggle to grow much other than anything leafy. You may manage to grow small carrots, but otherwise I suspect water and light will be the biggest issue, light in particular. Do consider lettuce j any variety of leafy stuff) mustard for the leaves , carrots, beetroot (for the leaves) and possibly peas (for the new shots and leaves which are edible and very nice).
You may at a push manage tomatoes but I suspect the crop will be small.
Did I read somewhere that you are in Canada? If you are then you will need to wait until spring because most plants respond to natural daylight and the lengthening of the days and require a certain amount of time off natural daylight to actually germinate and grow properly, not to mention temperature.
Also remember that having that amount of soil in your apartment is going to make your apartment damp. Plants really do not like soil drying out constantly.