You need to narrow it down a little. The US is a huge country and the hunting opportunities vary consideribly between the 50 states. I'm sure some states allow non-resident aliens to do do-it-yourself hunts. Alaska for instance requires all non-resident aliens to hunt with a registered guide, which increases the cost considerably. It's highly unlikely that you can rent a rifle anywhere. There's far too much liability for people to rent out firearms. Start out by deciding what your maximum budget is as that will dictate what you can and can't do. Then try and figure out what species you can hunt based on license fees, travel expenses, gear you may need to purchase etc. That'll help get you on your way.