Camp gear for a wet state with real fire rules
Plan to cook on a stove. ORC 1503.18 prohibits most open burning in unincorporated areas through March, April, May, October and November between 6 a.m. and 6 p.m., which covers a good deal of the shoulder-season camping year, and local fire departments can add their own rules on top. The Wayne allows small open fires except in extremely high fire danger and asks you to use a ring where one exists.
Firewood is regulated too: do not bring any unless it is commercially packaged with a USDA inspection label, though you may collect small amounts of down and dead wood at your site on the forest. In state parks, collecting firewood and using a chainsaw are both prohibited.