Help on buying a horse

My DH and I are looking at buying a horse for our children for 4-H and we know very little about this. There is one for sale at our county fair that we are looking at. It is a 25 year old quarter horse mare and is registered with papers. They are asking $1200 for her. She seemed to be very docile and well trained and let my kids (ages 6 and 8) pet her and sit on her back in the stall. We couldn't let them ride her at all since it was at the fair. The man who is selling her said she trained his daughter and others we asked said she would be a good beginner's horse since she is so well behaved. My concern is her age. How long do horses usually live? I'm worried about my kids getting attached and then losing her or having overly large vet bills. Is this a good price or are they asking too much? Any advise or other questions I should be asking the current owner would be great!