A bale of straw from a rural coop worked for me with tomato plants last year. Colorful too. Some vines rested on it and the fruit stayed off the ground. I get grass clippings from neighbors but only if they don't fertilize or use weed killer.

Straw is great, but if you're willing to spend a little more money buy alfalfa hay. You get two things with it - great mulch and top drawer organic fertilizer. Mulches this year's garden and breaks down completely over winter to make rich soil. Do this every year and in short while you won't need any other fertilizer. It's true and it works. See Ruth Stout's "How to Have a Green Thumb without an Aching Back," or "No Work Garden Book," she pioneered this method back in the 1940's. I've started doing it since seeing my sister-in-laws cauliflowers - prize pumpkin size. It's all she does.

Ruth Stout composts by tucking kitchen waste under the hay and letting it rot there. In the spring she lays down 8" of hay, pulls it back to seed, then uses it as mulch.

My veg patch is about that size. It takes at least a couple years to start decreasing the "seed bank" the soil may have. I have had great sucess by simply removing the weeds after it has rained, and before they go to seed. Some weed seeds stay viable for 20 years and tilling may bring some of those to the surface, so I don't do that but mulch a little and dig in compost as well as some shredded coconut hull. The coconut hull comes in a brick that you hydrate and expands 5-fold allowing for better aeration of the soil. That way the roots can go deeper and the plant gets more heat near the surface. Works for me.