Donna, your tomatoes, cucumbers, zucchini, pumpkins, and watermelon will be large plants and set out or sown fairly late. You have a chance to cultivate the soil a few times to kill weed seedlings. Even a light raking the last couple of times will tear tiny weeds up and lower the competition for your veggies.
It should be easy to get mulch around these 5. Newspaper or cardboard covered with grass clippings, for example, is very a effective mulch.
Lettuce can be started indoors and set out but it is probably easier to direct-sow the seed in the garden. Lettuce seed will germinate at just about the lowest soil temperature of any veggie - so, you can start it very early. You may want to sow some radish seed and plant onion sets about the same time so that you've got garden salad fixin's!
You should find your most weed-free ground to plant lettuce and make plans now on how you will get in there to pull out weeds. Don't "cram" the rows together. Mulch may not be the best thing for lettuce. Earwigs and slugs like mulch . . . they love lettuce.
Carrots, you may have the most trouble with. The seed seems to germinate slowly, even in the best of circumstances. Weeds can really crowd skinny, little carrot plants and pulling out weeds without pulling up carrot seedlings is difficult. Don't let the carrots grow too closely together, anyway. If you get a good "stand" of carrots, they will probably need to be thinned.
Here's wishing you the Best of Luck and a Good Garden!
Steve
