I wouldnt worry about coyote hunting right away.
As far as squirrels go, what are you going to use? . Most use shotgun (20ga is best or .22lr) Most hunters use .22 for numerous reasons, fine tune their shooting skills for when it comes to bigger game and not to destroy the squirrel or spend all your time picking lil shot out of it.
Is this public hunting or private property ? If public hunting, find the rules and regulations and if you need to wear orange (squirrel season usual coincides with bow hunters, so you want to be seen).
Dont go crazy with gear. If your hiking, take a day pack with food, water and enough stuff to stay over nite (survival bag), small first aid kit, fire starter, water purify, tarp for shelter and extra clothing.
Wear Layers, if your hiking, youll get hot, dont get sweaty or over heated, animals can smell ya and not good for you in the long run.
Jus wear some comfy cargo pants , good socks and hiking boots, and layers for up top (t shirt, long sleeve shirt, light jacket and then outer water proof layer), beanie hat and some gloves. Have a good knife, something small for gutting animals, dont need a bowie knife, 99% of the time, most use a folding pocket knife.
There are some tricks to shoot squirrels. One of them is, dont shoot them at a fork in the tree, the odds are they might have a hole there or get stuck in the tree, good bait for the birds, but if you want to keep it, wait til they are going up or down the tree or out on a limb. IF the squirrels are making all kinds of racket (and youll know when you hear it), the jig is up and they know your there and warning others, either sit down and wait til they settle (they may or may not) or move.
While the above poster was short and sweet with his reply, lol. He is right. Squirrel hunting is usually the first season ppl get in the fall to get out in the woods, most dont care if they shoot one, alot of times, its pre-cursor to deer hunting and they are actually scouting deer and popping squirrels along the way.