State residency is a tricky grey area and depends on all the details.
I'm of the opinion that your planning on being in OH more than a year ("staying for a couple years") makes you an OH resident. You are not the student, so the student exception doesn't apply. Not only should you be filing 2018 as a part year resident, you should be changing your drivers license and auto registration to OH.
Tax wise, it wouldn't matter much for 2018. You'll pay the same amount of OH tax as a part year resident or non resident.
For 2019, as an OH resident, you only have to file an OH return. As a non-resident, you'll have to file both an OH return and a return for your "home" state.
