Would like to second the newspaper/straw mulching with an additional precaution. I've found that the newspaper is favored by earwigs for nesting, and earwigs like to make a snack out of some plants. So I sprinkle ground eggshells around base of plant before putting down newspaper and again after spreading straw...they don't like the scratchiness and tend to find somewhere else to nest. Then if they still persists I sprinkle diatomaceous earth, which only works when it is dry. it needs to be reapplied after watering/rain.
Back to the mulching though, we sometimes spread the straw out on the lawn before we mow and then spread the clippings on the garden. SEems to prevent the grass clippings from getting matted and moldy and it chops up the straw too. This year, however, that method's been difficult to do because of the lack of rain, decreased mowing, and the only thing growing are "weeds"... and we don't need more weed seeds in the garden.