Forming an LLC

I am looking to start an investment company primarily dealing with rental properties at first and then I want to expand further from there with flips, commercial, and so on. I live in Ohio but plan on starting rentals and flips out of the state. I really want one business and one name. So do I start it here in Ohio and do business out of the state or do I start an individual LLC for each state I do business in. That sounds kind of crazy. Unless I could start a company in Ohio and have divisons in each state. Not sure how that would work.

Any help on this would greatly be appreciated.

Thanks!