I would like a complete well water test performed on my rural home water...
The Ohio Department of health has a page to provide information for a safe private water system. The basic things to start with are bacteria and nitrates. The site does go on to discuss other important parameters. The things you should test for depend on the things that are and have been going on in your neighborhood. Your local health department may be able to help you make that determination.
The Ohio EPA has a list of certified labs,