Few random ones which I can think of right now...
How many aircraft on fleet? <- If one goes in for maintenance, or develops a problem, you'll want to ensure you can carry on your training
How many instructors do they have in total? <- If one goes on holiday, you may want to carry on your training with another instructor temporarily
Landing fees? <- Some schools "include" them in the price hourly price, ask if they are or if you'll be paying a trip to the tower after each lesson, but the school I learnt at didn't
Pre-flight/lesson briefs included in the hourly price? <- I know of
at least one local school which charges extra for the pre-flight/lesson brief on top of the flying hour
What ratings do they offer? <- This will tell you whether you'll be able to do everything "in house", or whether you'll be needing to switch schools post-PPL issue to continue with things like CPL/ME/IR/Night Rating/etc. This will come down to cost anyway.
Classroom time for the exams? <- I did all but a quick "pre-exam brief" studying at home for the PPL exams, other people may perfer actually being sat down and taught
Availability going forward for your schedule <- If you can only fly on the weekends, ask how far ahead other students book in as you might need to be quick
I'll report back if I can think of anything else for you.
One super important point, and hopefully no-one disagrees: don't be lured in by an all-in-one payment package. Many schools offer this, and it may look like a cheaper way of doing it, but if that school closes it's doors when you're 5 hours through training, you'll lose every penny - I saw this happen twice during the 2 year period to get my PPL at my local airfield and know students who lost out. Pay on a per-lesson basis. ( Note: If you did do this but paid on a credit card, I do believe you would have some protection, but that would require your own research
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