I've incorporated my startup think tank Apriority LLC as a Deleware corporation. The fact that it is an LLC should be no hindrance to converting to a corporation once you are ready to go public (assuming that is even a goal of yours). I have plans on keeping my think tank private and spinning off corporate public businesses from the research done at it so that is the primary reason for my set up. The choices you make should vary with what you hope to eventually achieve with your new business.
That said, the reason I chose Deleware is that it is known for having a very pro business, light on taxes view on new company formation. They don't require as many book keeping rules (for LLC's) as some of the other states (my home state NY for example does) and many of their yearly fees for maintaining the incorporation status are lower than in other states. I just want to warn you I am not a lawyer, so make sure to try to at least consult a lawyer on the matter (I wouldn't pay for one, lots of free advice is doled out on line and many lawyers will talk to you for a few minutes before demanding green for additional services).
Finally, as far as I am aware the physical location of your business needs to have a US address, so you will have to have at least one such location in the US that you use to have correspondence information sent to. I used a service called "the company corporation" to incorporate my think tank back in 2002 and have been very happy with my service, not sure if they have services for out of country individuals but you can go to their web site and find out. There are many providers of similar services so shop around for a fit that is perfect for your needs.
Much success on your new endeavor, you can't succeed if you don't try.
Founder and CSA, Apriority LLC and numeroom.com