Get them to demonstrate their student turn-around time. How many schools advertise a 4 week CPL that actually takes 10 weeks? If they have nothing to hide, they should have evidence of recent students' training programmes.
I would pay up front, but no more than a few hours' worth of flying.
Make sure they can actually find/source an examiner. (Sounds silly, but some schools really struggle to get one in the right place at the right time).
Get a warm feeling about aircraft availability. If they only have one twin and you're down to do twin training, what is their plan if the aircraft goes tech? Do they have access to a spare? Is the one aircraft due an annual?