Well I don't know about Ohio but to my knowledge as a gas fitter in BC there is no "minimum" but you need to have some slope. 1/4" is plenty.
The only real thing you need to worry about is the length of the horizontal run. The lateral length of the vent connector will directly effect what size the vent shall be.
If you are just running a HWT (Lets call it 40,000 BTU) you can have a lateral of 10 feet or so with an overall vent height of 15 feet.
I hope this helps.