Unless you have more than one child you may not know any of the differences in driving schools. Even with 2 or more kids you might simply choose the same driving school because it's what your familiar with. But we all have busy schedules and monthly budgets to meet, so you should not take choosing a driving school lightly.
The worst way of determining a driving school is the cost. A cheap driving school can be just the same in quality as a more expensive driving school. Most parents do not learn enough about the school to access the quality of the school. A student "enjoying the class" does not mean they are receiving a quality education. Most schools do not allow parents to attend the class or ride along in the vehicles, so it is very hard to accurately know about the quality of education. Public driver education, as opposed to private driver education, is taught by local school district teachers and usually held in a public school. It is generally cheapest and is taught by certified teachers, but the scheduling is horrendous.
Scheduling is another extremely important issue that many parents easily overlook. When contacting a driving school be sure to get the number of drives and how long each drive is. For example, a parent told me they went with public driver education because it was over $100 cheaper than the other schools. They soon regretted it as it meant dropping off and picking up their student 20 times! (5 days a week for 4 weeks with 1 drop-off and 1 pick-up per day) Some driving schools pick-up students at their homes early in the morning around 5:30 in the morning. Some driving schools do as little as 3 total drives and some do as many as 8. 3 or 4 driving days sounds efficient but is not good for the student. This means 1.5 to 2 hours of driving each drive - this is way too much stress and information for a teenager.
The location of the drives are also important. I once had a parent not too pleased they had to drive 15 miles through rush hour traffic to get to the drive locations (the drive locations were on the same website page as the driving days). Be sure to ask if they let the student drive home or get picked up at home. There might be an extra charge but it could be worth it.
Ask how long it will take to finish everything. Some driving schools advertise certain time when the class will be finished - they are only referring to the class - the actual driving portion could take 2 to 3 weeks after the classroom portion is over! Years ago I instructed for a driving school in which it was common for students to continue the driving portion 3 weeks after the 30 hour classroom portion had ended.
Is it better for your student to take the classroom portion in an actual classroom or from an online course? Usually a driving school that has an actual classroom is best - usually. I have personally witnessed many classroom instructors, including instructors who are school teachers, teach absolutely horribly. Most online courses, except Idaho Online Driver Education, are not that good. If you enroll in an actual class, it might be hard and expensive to make up a missed class. If you miss a class some driving schools do not give you the permit until you have attended a class in the next session - possibly 1 week longer to wait.
The driving routes are also important. You should ask "Where will my student drive on each of the drives". I knew an instructor whose students did 4 drives: A drive 40 miles east on a highway, a drive 30 miles west on a highway, a drive 25 miles north on a state highway, and a drive 20 miles north on a different state highway. The student performed a total of 3 left turns and 2 right turns on a 1.5 hour drive! Each drive should be progressively more challenging and realistic.
A few other things to consider are rescheduling convenience and cost; what if the student fails the classroom or driving; safety of the vehicles; and instructor experience. Rescheduling can be costly at up to $50 per hour. Some schools like public driver education have a very strict pass/fail policy. Some driving schools have vehicles that aren't very safe. And generally the more experience the instructor has the safer your student will be and the better education they will receive.
