I guess a good question to ask would be, "How stubborn are you?"
I'd ask:
Do you like flying? Are you going to be excited to do my lesson just because it's another chance to go fly? What are your most and least favorite parts about instructing?
How flexible is your schedule? If another student cancels, would you be willing to contact me and ask if I'd like the spot?
How full is your schedule/is this a full-time gig? Are our schedules compatible?
What's the craziest/scariest thing that's ever happened to you while flying? How did you fix it?
Things I'd look for:
Do our personalities mesh at least a little bit?
Do I feel like I can trust this person?
Can I engage with this person and follow what they're talking about? Do they explain things well?
Does this person seem like they know what they're talking about?
Are they open to admitting what they don't know off the top of their heads and willing to find or help me find the accurate information?
I guess for me, past student history isn't that much of an interest. Both my first and my current instructor are brand new instructors and it's actually been pretty cool. I'm probably going to be my instructor's first student to take a checkride. I have to admit, though, it was more of here's the only available instructor, do you want to schedule with them? rather than a conscious choice. I've gotten lucky, though, and got the new ones who are more on top of everything because of how new they are and the type that goes to more experienced instructors for help when we run into issues.
Hope that helps!