Legal Question in Business Law in Illinois

You are always free to form your entity in any state, even if you were still residing in Illinois. If you are "doing business" in a state other than the state where the entity is formed, then you might have to register as a foreign entity and pay taxes in that other state. Also, to the extent that you use a pass-though entity, all or a portion of the income may end up on the tax of the state you reside in, even if the entity is formed elsewhere, particularly if you are the one providing the services to run the business.

Since your business is an e-commerce business, it is probably unlikely that you are "doing business" in another state in the traditional sense but states are aggressively expanding what they consider to be doing business for both sales tax and income tax purposes. Still, since you are currently residing outside the United States, you would probably want to pick the most tax-friendly jurisdiction, taking both sales taxes and income taxes into account.