Most edible plants need a lot of sun, so you might struggle to get any sort of a crop. Best thing is to regard it as a fun experiment, rather than a way to feed the family. If possible, when it gets warmer (?), stand the plants outside on an external window ledge for extra light. Don't let the compost dry out. As with growing any fruit or veg, (1) only grow things you like, and (2) grow for taste. You could try herbs (basil, parsley, etc), cress, leaf salad. Not sure if new potatoes would work, but worth a try if you have the room. Personally, if I was going to try one thing on my windowsill it would be "Gardener's Delight" tomatoes. They're small and exceedingly tasty. I grew them for years down my allotment until I was beaten by tomato blight.
http://www.bbc.co.uk/gardening/digin/your_space/windowsill.shtml