Dave, I just went to the Ohio BMV site. According to what I saw there, the Thomos Targa LX is NOT considered to be a moped in Ohio (because it generates more than 1 brake horsepower and goes more than 20 mph on level road). They actually have a list of bikes that are qualified as mopeds. If it ain't on the list, you can't legally operate it as a moped in Ohio.
Anyway, here is a link to the Ohio BMV website:
Also, the guy you're buying from is responsible for getting a duplicate title. If you walk into the tag office with nothing but a bill of sale and his old registration, they won't be able to title the bike. A duplicate title costs $5, which is pretty cheap, so if the seller won't handle it, either there is a problem with the ownership of the bike or he's too lazy. Your policy should be...no title, no sale.
Whatever you decide to do, be aware that Ohio considers the LX to be a motorcycle, so you might get hit with license endorsements, insurance, inspections, and stuff like that.
My opinion, $500's not too much for a 96 Tomos that's been taken care of. I sold a 95 Targa step through last month for $600 (7,000+ miles).
I hope your deal works out for you. Good luck.