Length of Stay and Invitation Letter

Hello - I'm a U.S. citizen and I want to travel in China as a tourist for about two months. Before I buy my airline ticket, I want to make sure that I can stay that long (assuming that I qualify for a visa). Can I get an entry permit to stay two months?

Also, I've seen mention of needing an "Invitation Letter" in order to get entry permit. I will be traveling independently (not as part of a group or being hosted by someone in China). If I have a hotel reservation confirmation for the first week or so of my trip, will that be sufficient, or do I still need a "Invitation Letter"?

Thank you for your help!