Ground covering edibles?

I am sq meter by sq meter digging up and clearing a very overgrown garden. I know that weeds will reappear if I just leave it. Is there anything edible I could grow (possibly through holes in an anit-weed fabric) to cover and utilise each section as I clear it? Then next year when I have a larger area cleared I'd like to sow gr of some sort. Replies for first time gardener PLEASE .. so nothing difficult (or expensive). THANK YOU in anticipation.