My guess is wood chips would probably do it - although you may have some weeds get through, probably not much. You could lay down plain cardboard first and the wood chips on top. The cardboard will eventually break down without you having to discard of it later as you would with plastic.

Newspaper or cardboard laid down and then covered with wood chips would be a good idea, plastic sheeting may keep air and water from getting into the soil here the Raspberry roots need them. Depending on which grass you have it may grow back or it may root in the mulch as other unwanted (weeds) plants will do. Mulches, such as wood chips, help keep unwanted plant growth down but will not eliminate them.