What would/do I look for??
First & foremost I'd be watching the person working with other horses and finding & checking out other horses who have been trained by the person. I look for someone with a good knowledge of horse behaviour & bodylanguage. Someone who is considerate & respectFUL of the horse. Someone who will enhance & reinforce the horse's positive attitude towards people & the 'work' we want of them, and will help the horse become comfortable & confident with everything, rather than just forcing them into stuff & making them 'work'. After sussing them out & seeing them work with other horses, I would have a lesson or 2 with them, let them work with my horse in front of me, before I'd ever consider leaving my horse with them.
References, are a start. But knowing the wide variety of opinions on what's good, bad or indifferent, I wouldn't put my trust in refs alone - been there, done that once, one of my horses still has the mental scars to prove that approach wrong, after only 1 week of the wrong 'training'! I also would be hesitant of, but wouldn't definitely rule out people with little experience so few references. If I thought they had a great attitude & understood enough of the principles, theory, I would probably give them a chance, at least in front of me.