I have seen lots of horses over the years that would take care of children
and when mounted by a rider who knew there stuff, the horse would wake up
and be a fun ride.  I think the answer is training and not too young.  Look
for someones horse that is a fairly good rider/trainer.  Look for quiet
ground manners.  
As a mother of two sons who rode in their youth, but no longer ride, and a
4-H and Pony Club leader, I really suggest you never overmount boys.  Girls
seem to handle that much better, and have a better understanding of
animals.  Of course, I am speaking in generalities.  A lease is an
excellent idea.
Have fun shopping,
Bonnie Short