Being a smaller (for now) independent studio, I have so far avoided implementing a strict studio policy, preferring to work out an arrangement with each family with which we are each comfortable.
That said a couple points are worth mentioning.
Often we will do a trial period (usually between 4 to 8 lessons) before committing to a set number of lessons over a longer term (usually the rest of the school year).
For trial lessons, I am happy to be paid the day of the lessons.
For the longer term, I need to be paid in advance – usually the longer the better for both of us as it will reinforce the commitment on both sides.
Missed lessons due to illness
From experience, the student being sick the day of is potentially the stickiest issue.
A good solution I find is for me to still be paid for a cancelled lesson (I don’t teach as well when avoiding getting sick), with you having the option to make it up after our other scheduled lessons (usually in June).
This way, I can count on my income (and concentrate on teaching), while you can recoup the lesson if it is still a priority.
For lesson times ending before 3:30pm on weekdays, I can usually offer a reduced rate.