Let's first define the three:
Sole Proprietor - An unincorporated business owned by an individual in which there is no distinction between the owner and the business.
LLC - business structure that is filed with a state in which the business is a separate entity than the owner.
S Corp - an entity which elects to be taxed as a corporation. The entity must first be formed as an LLC.
A big benefit to being a Sole Proprietor is the ease of forming it. This type of business essentially doesn't require anything besides business activity to be considered a Sole Proprietor. The disadvantage is the lack of protection. Anyone that does business with you can sue you for any reason and can take your personal assets such as your house, car, bank account, or even your retirement.
The benefit of having an LLC is the protection it provides. If a client decides to sue you, they can only go after your business assets and not personal assets. Forming an LLC does require filing it with the state, but this is a fairly simple process.
Electing to be taxed as an S Corp is very beneficial once profiting a certain amount. This election can save you thousands in taxes once you are at a certain profit level. Generally speaking, if you are profiting at least $50K you should be talking with a CPA about the benefits of making this election.