Fully internet-based business: where do I register and why?
First of all you do not need to register your company in all 50 states. In fact, to start you might choose any state as your state of formation (for example many online businesses incorporate or organize in Delaware or Wyoming). Then, as your business grows and you start open offices and hire W-2 employees (not contractors though) you would need to file for authority to do business in those states where you will have physical presence (its also called "foreign qualification" or "forming foreign entity").
As far as income taxes go, LLC is a pass through entity, so you and your partners would receive member distributions from your company's profits (or losses) and then file your individual taxes on those and other profits in your respective states. I would recommend you to consult an accountant to learn more how to deduct your business expenses and how the income tax issue would be handled with members spread all over the country.