The difference between NE Ohio and SW Ohio is pretty significant, but either way you'll want a couple options.
Spring/Fall jacket. You'll especially want this if you're not used to Ohio weather. The temperature drop from day to night can be pretty dramatic and there is nothing that sucks more than going to happy hour in 60 degree weather with only a t-shirt and then in an hour be freezing in 40 degree weather. Most common option for this is a Northface or Columbia jacket. Damn near everyone has one or the other. Since you're not used to the cold, compensate with a slightly thicker option or just make sure you have layers to put on when needed.
Lighter jacket/hoodies/overcoat/rain jacket. Somewhat of an alternative to #1, you'll want a couple options here. Hoodies are great for chilly ~60 weather and there are plenty of options from cheap to high end. Additionally something like a rain jacket or light overcoat is always nice for those late October rainy days when it's not too cold yet.
Pea Coat - most versatile option. Can use as an alternative to #1 or when it's too cold for the lighter jacket.
Parka/Carheart/Whatever. If you're in NE Ohio you're going to want to forget all fashion sense (unless you're willing to drop some serious cash) and get the warmest, well lined, heavy ass jacket you can afford. Add hats, gloves, heavy socks, and boots. If you haven't experienced 0 degree weather with the wind blowing, you're in for a shock. You'll luckily have some time before you have to deal with this, but just know when it's that cold, NO ONE will judge on your fashion choices to stay warm. Except maybe your hat. So, get a cool hat.