I can attest to the "critters" liking straw. I had a raised potato bed which had 12-18 inches of straw on top. Great big potatoes, but also some were nibbled on by something because they were easily accessible in the straw.
I'd still go with the straw, either used to build the walls of the bed or loose straw added as the plants grow taller. This works particularly well with potatoes, but other plants benefit from a straw top layer.
Opinion: Planting directly in the top of a straw bail will mean that the plants need extra nutrient addititions since the straw, by itself, is pretty low in everything but nitrogen. A manure tea is a good start and adding trace minerals will make the plants happy.