paolo11 wrote: Is there an optimum number of coaches and doctors? Does it depend on player numbers or is it simply the more the better? What is the maximum number of each?

Once you have your finances settled (all VIP and Executive seats fully built), and your training halls complete, you should probably hire best coaches. I have coaches who have 20 at everything except at kicking.
I would argue it is cheaper to build in redundancies than buying doctors, but if you have a really small and lean roster, then it makes a lot of sense to have the best doctors.