I'm going with composted cotton burrs as a mulch. As for mulching the garden, it's really not necessary, but it does help with cutting down the weeding. As for using the clippings, leaves and shredded paper, I'd compost it and use it for next year. It's been my experience that those three items, are about the worse for a mulch. They tend to cling together and make a waterproof covering.
Will

I mulch with squares or sheets of cardboard.

I cut a square of cardboard a few inches larger than the plant's square, then cut diagonally in the square until I get to the center. Once I'm at the center I cut out a largish hole for the plant to grow thru (I water the plant thru this hole as well). I overlap the cardboard or use sheets (with holes cut out for the plants) so that no soil is visible except thru the holes.

The cardboard works great for me for several reasons.

1. It is an excellent mulch in that it keeps moisture in, and prevents weeds from growing through.

2. I can water in the hole and prevent soil from splashing onto the plant leaves.

3. Fruit can lie on the cardboard without any risk of soil disease, mold, or rot (the cardboard dries out quickly in the sun, so it is almost always firm and dry).

4. It doesn't need to be renewed. The cardboard will last the entire season unless it becomes covered with OM of some kind (leaves, grass, or even dirt). If it is covered or becomes a layer it will begin to break down.

5. The worms love it and will move into your garden if it is accessible to the ground (no bottom on your raised bed).

I would recommend waiting until your plants have grown a bit before mulching with cardboard (unless you already have experience with the stem size) so that you can better judge how large the center hole should be.

A light, even sprinkling of grass clippings. It won't get hot if you use common sense and don't put it down too thick when they're fresh clippings. If you're worried, dry them first on the driveway.