From what little experience I have with nature photography you have already identified the 2 main points.

The longer the lens the better (even with a 500mm lens a small bird will only fill about 25% of the frame from 20 feet away.

So that also brings us to being as close as possible. Many of the best shots are taken from hides and lots of patience over several days, also many people bait the scene within distance of the hide to get the birds there and keep them there long enough to shoot. Others will set up "false" perches for the bird to land on again within distance of the hide. 200-300mm is fine with wild birds that have become accustomed to human presence allowing you to get reasonably close with slow movement to get the shot.

Many of the "better" pictures these days are I tremble to say produced by digi-scoping. Hope that in part answers your question. I'm sure there are many more experienced photographers here that may be able to add more information. Good luck it's a very frustrating but rewarding area of photography.