We're actually going through the same process right now. I'm not a tax expert, and this is NOT legal or tax advice, but here is what I've figured out to this point.
First, you need to register as a business with the state of Tennessee and the local jurisdiction. You don't need to be an LLC or anything.
You also need to register to pay state franchise and excise taxes (annual business tax).
You have to register with the state for sales tax collection (9.75%).
Lodging taxes are 3%, filed and paid monthly. If you're in Sevierville, Pigeon Forge, or Gatlinburg city limits, you pay to the city. If you're outside those towns, you pay to Sevier County.
The city of Gatlinburg also charges a Gross Receipts tax, of (I think) 1.25%, filed and paid monthly. I'm not sure if the other towns in the county do the same.
Here are a couple of web pages that might help:
https://secure.tennesseetrustee.org/index.php?entity=SEVIER&state=TN&page=93http://gatlinburgtn.gov/finance/finance-department.htmlVRBO doesn't collect or remit taxes for you. So you would need to add a 12.75% tax rate to your listing (14% if you're inside the Gatlinburg city limits).
Airbnb collects and remits state sales tax for you, so you'd just need to deal with the business registration, franchise and excise taxes, lodging taxes, and gross receipts taxes.
It's more complex than I thought before we dove in, but I think it won't be too bad once we get it set up over the next few weeks.