I use Servo, auto-focus set to tracking, shutter speed at 1/1000 for slow flying birds, 1/2000 for medium size birds, 1/4000 for hummingbirds.
I also shoot shutter priority , Auto-ISO as the lens will be wide open anyways at fast shutter speeds.
For birds in flight, I use "Case 2", zoom way out with incoming birds, and once the camera is tracking the subject,
then zoom in. Here is an example from last week with a shortear owl zoomed in and tracked at 800mm.
For perched birds, waterfowl on the water, etc. I use the Pre-burst mode which stores in memory shots that I would miss otherwise the instant the bird is taking off. Hope that helps.