I am certainly not the best here, but this is what works best for me (using D750):
For action/BIF:
Manual mode, auto-ISO enabled. base setting is 1/2000 and f5.6, but I will often change those.
Back-button-focusing enabled, AF-C with 9 points normally on (will change this often too). Video button is set to change sensor area mode, Preview is set to change white balance and Fn is set to DOF Preview but seldom used.
In this mode I will tend to use the central focus points and crop later, as even with a 500mm lens I am not often close enough to the birds.
For more static subjects:
Aperture Priority with Show ISO/Easy ISO enabled, back-button focussing enabled (actually this is enabled across all camera modes), AF-C with single-point on. Base setting is f5.6 and ISO400, but will change these often.
In this mode I will often move the active focus point for composition, unless the subject is small or far away, as I believe the centre focus point is probably the most accurate (it is the only one on which my AF is fine-tuned.