It looks to me as though there is nobody currently gardening here?
I would look for areas with the most broad-leaf weed presence. In community garden beds, people are free to spray all sorts of stuff on their plants and soil. since this plot looks like it's been fallow for some time, the areas with the most vegetative growth probably have the least amount of residual toxic gick in the soil. Beware the clear spots. They might be weed free growing beds ready for planting or they could be dead zones. I would plant these with a cover crop. Mustard, barley, rye, field peas, whatever and see how they go in the first season.
I currently have use of an area too big for me to put into full utilization with the resources at hand. So I rotate small grains through the beds each year so I have a resource of good straw that I know is chemical free.
I also plant a lot of annuals for the purpose of seed production. Radishes, dill, spinach, fava, etc all work well. You might like to consider biannuals for seed production like beets, carrots, parsnips etc in the extra space. The plants like parsnip, cilantro, and dill attract predatory wasps which help out in the garden too.
I also plant a good quantity of brassicas like Brussels sprouts. Not because I harvest them, but because we get ground hogs, rabbits, and deer and I found that they like to eat brassicas, and if there is a good quantity of them in the quiet corner of the garden then they leave my other plants alone.
Some sort of mulching is going to save you a lot of labor. If there are beds with clover in them, I'd be inclined to leave it be and simple plant into it. It doesn't grow tall and shade out your crops like grasses do, and it acts as a ground cover and Nitrogen fixer.