Straw should work very well...just make sure it isn't hay. Hay contains grass seeds that will take you the next ten years to get rid of! We have to mulch here in south Texas and I wish I could find straw to use!
Straw is good, IMO. If you put it on real thickly and have a vole problem you will have a bigger vole problem, but that is true to some degree of any organic mulch.
Tip: OaklandCityFarmer is right, straw often (depending on the type of straw) can be somewhat reluctant to break down and thus difficult to till in come Autumn. One thing I've had really good luck with is to dump a layer of manure, it can be fresh if need be, atop the straw in the Fall and just leave it there (don't till). Then in spring when the soil becomes workable, dig or till it all in, it'll be easy. You do lose some of the nitrogen value of the manure this way unless you mulch on top of *that* with dried leaves or dried-out not-gone-to-seed weeds, but oh well.
We use straw and it works just fine. You can also put down a section of newspaper under the straw and it will help even more. Just try not to disturb it after it is put there and don't skimp on the amount.
Thanks for the replies - straw and newspapers it is. Unfortunately I don't have access to manure so I'll make do. I do have a shredder and could mulch the straw into smaller pieces.
Here is picks of my goatpoo hay put down over cardboard between corn rows.
DH and I get the boxes from the VFW.
Any weeds that do manage to sprout come up easily by hand as the ground under the cardboard/goatpoo stays so soft I just give a tug and it comes right out.
I used wheat or oat or rye straw ,not hay,around my tomato plants .I didnt tear it all up,was used in books about 2 inches thick.Put grass clippings around the plant.I got this idea from a book called How to grow world record tomatoes.