Luke,

I would assume you want to know if its possible to have a company registered by a Non-US citizen. The answer is, of course, yes, you could register such company and use it for your international business. As far as taxes go you would need to obtain ITIN (individual tax ID), and pay taxes on the income received from your US company on your personal tax return (you would do it when you file your first year tax return).

Depending on your activity you might want to maintain two entities – one in US and one in Italy (but for that you need to know if having an Italian entity to manage the Italian side of the business would give you any benefits). The relationship between two companies could be regulated using written contracts between those companies (even if both are owned by same persons).

The cost of registration depends on the state of formation. The choice of state of formation for your business depends on how you plan to organize the physical side of the business, meaning whether you plan to have employees and/or office or not. If your US side would consist only of a website you might consider Wyoming or Delaware as your state of organization. Keep in mind that having virtual office in any specific state might require you to register in that state (it greatly depends on how broke that state is).

You are welcome to ask more specific questions, we are here to help.