Mulch for rasberries?

I planted some rasberries for the first time last year and they look to be doing fairly well this year. Do people usually mulch them and if so what with? What about the following:

- I have a steady supply of wood shavings/sawdust in small amounts from our guinea pigs
 - grass trimmings?
 - privet hedge cuttings?
 - bagged up leaves from last year that are only partly decomposed?

I used Straw based fresh manure last year.  Seemed to work for me.

All you really need is something that will help keep moisture in the soil, supress weeds, and not blow around if it dries out - having nutrients in the mulch is a bonus, although you can top-dress the rasps with a general fertiliser before you mulch them anyway.

I put well rotted manure or compost round in early spring & then top up with grass clippings in the summer to keep in the moisture (I have a very big lawn )