Someone responsible who I feel would get on with my horse, has the same goals, and ambitions as myself and someone who is experience with lots of common sense. I would expect them to handle my horse firmly but fairly and not molly coddle him and talk in stupid voices to him. By the same vein I would expect them not to shout at him all the time too. I would not want them to hack him out (he is not very trustworthy on the road) nor would I be keen for them to transport him to places, but I wouldn't mind doing that on the odd ocassion for them anyhow.
Someone who's capable of looking after the horse, riding him and dealing with his quirks. Some one who can afford to keep him and makes the right noises about keeping him the way I want him to be kept.
I found it quite difficult as when people are looking to loan a horse they don't seem to ask the same questions as if they were buying & I had to grill them before I would let them see him etc
Both, easier face to face but firstly asked the obvious on the telephone without being too rude. Ie. what did you want him for (in my case he's not aloud to do much jumping), is he kept at home or livery, have you had horses before etc.
When i looked for sharers i looked for people that seemed kind and quiet in their riding and handling as i worried that when i wasnt around if they were really forceful and loud then thats how they would act with the horses. Also i would only ever have older people as loaners as kids are too irresponsible and unreliable alot of the time. Its not that much use asking about people on the phone as most people say their quite advanced, ridden for years etc and then you see them ride and they may be advanced at a riding school but are complete novices on non riding school horses.
I look for someone who has a similar riding style to myself; someone who's quietly confident in their riding and handling. I find the ones who are a bit down on their ability are generally better than the ones who profess to be superstars.
When I watch them ride I ask myself whether they would be able to handle my horse if she played up - if I just can't see it I'll say no as I don't think its fair on them or the horse if I think my horse might damage their confidence (she's that type lol)
I don't tend to ask much on the phone, other than height and weight. I prefer to take them at face value on the day