It's always best to collect wood when it has recently fallen for your walking stick project because the rotting process have not started. Collect wood now to make walking sticks in the fall. Do not start standing or carving the wood when ti is green. You need to give the walking stick wood time to cure (release water) which can take several months. We recommend to collect wood now and remove the bark when the wood is still green. Willow, aspen and similar wood is a easy peel job to remove the skin/bark while the limb is green. Once it start drying it's much harder. No you do not have to peel the bark now if you pan to leave most of the stick in it's natural state.
When collecting wood to make your hiking stick or walking staff think about the end result; are you planning to carve the wood, wood burn images or other? Look at the shape of the limb and see if it interesting or has a natural area for carving. Many people collect saplings and use the root ball in the walking stick design. We usually use limbs only because it does not destroy the whole tree. However, some types of trees are fast growers and if there is an over abundance of a tree type in an area thinning do wonders to allow light in for other saplings.