Well, Congrats for getting an Arab
I would want to see the horse in different situations, how it behaves in stall/ pasture, around other horses and people. Have the owner tack and ride first, watch for general behavior, any quirks, like pinning ears when saddled, etc, then ride yourself, of course. Ask what the horse has done so far, trails, shows, schooling.
If you like what you see, schedule a PPE, with a vet you know and trust, to rule out health problems before purchase.
Take pictures, might help you decide.
Good luck, and have fun