You could hunt black bears and possibly caribou but you won't be able to drive to any areas that hold caribou, unless you hunt the 40 mile herd and that is a registration hunt which can be closed the day after it opens. Not a lot of areas open for moose in August either and the one's that are, get pounded by the locals. Your best bet for either a caribou or moose is to wait until September and do a fly in.
I'd also recommend bring a bolt action rifle, 30-06 will do the trick and ammo for it is very easy to find up here. Good luck.
