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If you don't already own tents and cooking stoves it might be worth renting?
The US seems to like single skin tents a lot more than we do in the wet UK. Less rain so they work better over there.
A multi-fuel stove is your best bet if you want to buy one that'll work everywhere.
MSR Whisperlite is great but as they are a US company you'll probably get it cheaper there rather than buying it here.
Mr_Sworld
You'll need a permit to wildcamp in the US National Parks and you'll have to invest in a food storage system to keep the bears away from the tent.