Look for natural products from a local landscape supplier. Things like pine bark (nuggets), shredded bark or recycled hardwood are about the best for weed suppression and moisture retention. And it looks nice. One of my suppliers gets mulch from recycled, shredded pallets from time to time and that works well. Or you could go with compost from your city/town if they have it. At the landfill in this area, they have a huge composting field and we can buy it by the cubic yard for cheap.
Please avoid cypress mulch. It works well but the commercial producers of it are destroying the swamps in the south just to make mulch. That destroys our environment and increases the chance of flooding.
Cocoa hulls also turn moldy pretty quick and form into clumps if too damp. Dyed muclches have colourant agents but most producers won't say what chemicals they are using. (I have 1 client who insists on the black-dyed mulch, even though I've tried to talk her out of it. It leaves awful stains on my clothes and tools.)
I think I would avoid grass, leaves and straw just because it doesn't look as tidy in raised beds, unless you don't mind the look.
