There are many hotels, ranging from the extremely inexpensive (€10 per night) to the luxury. You won’t discover the cheapest ones on the internet; the only way to book them is to phone personally, but you’ll need to know Russian at the very least.
Except for Burabay/Borovoe in Kazakhstan, there are practically no camping areas. Due to the vast number of deserted areas, you may, nevertheless, camp virtually everywhere. The landscape is stunning, but due of the very hot heat, bring lots of water with you since you might easily spend several days without seeing anybody. If you are camping near a nomadic tribe, ask for permission to remain nearby; you will not be denied.