Using chipped limbs in the garden

I have several different types of trees in my property. They all have a limb or so that are dead. As such I will be cutting them back to clean them up. I just got a wood chipper and plan to chip most of the smaller stuff, and cut up the larger stuff for backyard fires.

My question is about the chips. Can I chip them today and tomorrow put them in my garden? Can I use all the limbs from all the trees, or are there some that I should avoid? When laying the chips down, how deep should I have it?