Should I do anything to soil before applying mulch?
Don't pile it too high around the trees. Don't let it come in contact with, or near, any wood on the house. Make sure you maintain grade away from your house.
Some will put weed barrier fabric/plastic under mulch. I have found weeds will still grow on top of mulch. Friend uses Preen before mulch I think. I just weed first.
The key around trees is that the "root crown" is exposed. This is the transition point between the trunk and the roots. Too often people just pile he stuff on which can harm the tree and lead to bark rot.