Hi Suzie, if you already have grass sward up to the trees I would advise you leave it and just ensure it is kept short. Mulching serves two main purposes, the first is to add nutrients and organic material to the soil and the second is to retain moisture within the soil. Unless the trees are showing signs of decline there should be no need to alter the existing soil and grass works reasonably well at retaining moisture (bare soil should be avoided). If you do decide to add mulch wood chip is good but make sure it is well composted also check the source, you don't won't to import pathogens such as Armillaria or Silver leaf.