It does vary state by state. As for an LLC, you do not have to have the firm domiciled in the state you live in. Believe it or not, Wyoming is one of the best states to register an LLC in. Nevada is great too for a small business, but there are some hidden fees that really rack up. Delaware, of course, is the #1 state for large public corporations.

As for business structure -- go with an LLC right off the bat and not a S/C-corp, unless you plan on going immediately public, which is pretty damn impressive if you do. The benefits are enormous for an LLC. They combine the liability protection a corporation has and the flexibility a sole proprietorship has. Fees are pretty cheap. LegalZoom can file for you for like $99 + state fees. MAKE SURE YOU HAVE A LEGITIMATE REGISTERED AGENT. The reason I say this is if you do business in multiple states, you have different tax liabilities in each state that you'll be on the hook for. The RA helps you sort that stuff out.

Also, some states don't allow single member LLCs (nevada, delaware and wyoming do), so you'd have to get a legit business partner. Also, one member (you, if you're a single member) has to take point on tax issues. Their SSN is to be collected upon registration and they'll be appointed the "tax matters" individual, thus handling any issues that may arise with the IRS.