Hi Vince, all very good questions.
I started hunting not too long ago, and had similar questions. First things first, to hunt Sterling, you will need a parking pass, its $5 for us hunters an that'll enable you to park there during hunting season. To hike, you do not need this parking pass. This pass will be good for both small and big game.
Secondly, firearms are not permitting in Sterling until November I think. Despite the season opening for small game opening early September, you will not be allowed to hunt there with a gun. I do believe a bow is OK, starting Oct 1st. You'll have to look that up or someone here can chime in on the exact details.
The other popular spot for hunting is Stewart State Forest located in Windsor township in 3M. This area does not allow the possession of rifles and there are special parking rules that must be obeyed as it does get crowded during small game and big game seasons. During big game, you are allowed to drive into the forest and the hike is relatively short.
I hope this can steer you away from trouble and get you started.