personally: Advertisements, post-counts, "sounding" experienced doesn't much that much. Might contact those with good advertisements, appear to be "good" tutors but a lot of them (tutors) don't really care about anything than making money. I think people will make a long-term choice based on the first few lessons. ( see if it suitable, can understand them, see if they know their stuff, their attitude towards teaching u and I think most people will look for help outside the tuition hours - proofreading, questions)
probably general: A lot of people look for those with high grades, good study scores, good results ( for those that have recently finished VCE) or for professional tutoring - probably cost and experience.
I mean once again, all that is just what you initially think. You wont stay with that person with the high score if they cant be bothered teaching you properly or if they are incapable of explaining things to you in a way that you can understand.
Parents - they probably are willing to spend a lot more money to get you some better education/tuition because they want you to do well. So they'll probably choose someone who they think is good ( based on experience, qualifications probably) or let their children choose.