The only thing I know for sure about your question is that you are legal to own a handgun at 18 in Ohio. However, it is against the law for you to attempt to purchase a handgun if <21 and it is against the law for ANYONE to transfer, sell or give you a handgun if you are <21. But, if you moved into the state with a handgun that you already owned and were >18 at the time, it would be legal for you to possess that handgun and to open carry that handgun.
Nevermind. Black powder revolvers are handguns in Ohio.
Here's where your statutes are to read yourself: