New Castle is a great facility to learn about the sport. Comet Kart Sales is the shop that can get you the equipment you need to get started in the sport. Your son would race in Junior categories, which is 12-15 year olds. To start, I would recommend a Yamaha engine. This way, he can use the same engine as he gets older.
For Ohio information, contact Adreniline Karting. They can breakdown your options in Ohio.