You don't need a very big compost bin. With a community plot, that could be an issue, but 5 gal. paint buckets are about right for hauling the completed mixture. You can put damn near anything you eat in the compost except for animal parts and remains (egg shells excluded). Fruits will draw hornets for a while, but they really enrich the compost.
Even if you compost, you should add a few things (organic). Powdered kelp (meal), greensand, gypsum, calcium, potash, alfalfa meal, and if you don't mind that they're animal byproducts, blood meal and bone meal. There are also general mixtures available. Whatever you put on, use less than recommended and apply it more frequently, and gently stir it in if you're applying it as a top-dressing. A lot of it will run off if you overdo it and you can burn the roots, especially with nitrogen.
The other thing to do is get a SHITLOAD of radish and lettuce seeds and plant them all throughout the year, in and around the plants. Both produce a massive network of fibrous roots that break up and build up the soil. Don't worry with harvesting them. If they are in the way when it is time to plant something else, turn them into the soil. I've turned heavy clay, rock and sand, and shale beds into fluffy organic beauty in about three years each. The sand and rock took a little longer (NH). It takes time. And don't worry too much about weeds if the plants are getting enough water. The weeds produce roots too!!
Crop rotation is also beneficial, but keep the nightshades (tomatoes, tomatillos, peppers, eggplant, potatoes, etc.) in the same spot. They do better that way.
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