I'm good w/ Dave's recommendations relative to BiF's & other moving- target shots, but I prefer AF-S & single (center) point focus for stationary (perched) shots.
Generally use a 300 f/4, mostly w/ a 1.4x TC added. I can get a decent bird shot from a fair distance. Often the target isn't much larger than the viewfinder's single-center sensor indicator. More times than not, there in a tree amongst branches/limbs, w/ the slightest breeze making everything dance. Think going AF-C, dynamic 9-pt set-up under these circumstances will make that a tough shot to get.
Set my U1/U2 modes up specifically for stationary & moving wildlife, respectively, U1 is I've described + 1/800 sec shutter priority and U2 as Dave suggested + 1/1250 sec shutter priority.
I suspect there is not a uniform set of AF settings that all would vote for.
Mostly I use similar setting to Dave.
I also use the AE/AF set to Focus, and use my thumb to control the focus. But... I shoot small birds in bushes and on branches, mostly. Don't really do BIF, (too fast those little things). Tripod mounted, using a Markins 20. (Lovely head, and it balances the 500mm very well, on most days I would not have to over tighten it.) I also use either MuP, or Shutter Delay. With a remote release, the sharpness is much better. The few that get away, I figure I was going to get unsharp anyway. I don't shoot mulitburst, one good one is indeed one good one.
.. I set out to discover the inventions of God. -John Muir