For a new manager (i suppose you mean a new manager, instead of a new player, right?), I think lvl 3 doctor is enough.
Deciding the level of a doctor is quite complex, and it's about how much you're willing to pay in order to reduce the duration of injuries.
One who hates to see his players get injured may get lvl 6 doctor, but sarcrifice a lot of money, and one who doesn't really mind seeing his players get injured may get lvl 1, 2 doctor.
I have lvl 3 doctor though. I could get higher level doctor, but I personally don't feel that it's worth it. But ofc, there's a risk of long injuries and later regretting for not getting a better doctor etc etc.