Interesting discussion. I don't solicite for students in any way. So the way they hear about me is through a recommendation. I've thought about doing something, like a parade float with students (small town) but then I feel like I would get every person who even had an inkling of lessons. Weeding them out would be much more difficult.
I feel that those who seek me out are serious enough. In our first conversation (after a few possible rounds of phone tag), I give a brief overview of myself. I ask all sort of questions. Do they have a piano and if a keyboard does it have a pedal, 88 keys and is touch sensitve? What other activities involved in? I'm not the one to determine if they are too busy to handle lessons but make clear the importance of consistent practice. I state my fee: lesson rate and total tuition fee. I want my families to know just how much it is going to cost them over the period of the year, and not get into the middle and have a cost issue. I then send them a copy of my policy which includes the full activities going on in my studio and expectations.
At their first lesson, I find out from the student where they are at in their music knowledge. This is still to be refined on my part, but I do have a good sense of how much they know. Transfer students get asked a lot of questions through their first lessons. I'm just as new to them as they are to me.
I feel like some parents sign up kids for piano like a season of a sport and we'll just see how it goes. I don't like when students have a short time with me, but I can always fill their place with someone else who is willing to pay more and work more.
I'd take FLMikeATT as a student but two things would have to be understood. Although not all music has to be memorized, memorization will be a part of the lesson along with performing in public. I might not have written the book on how to totally fail at both these things, but I was definitely a contributor. You can do it!