You asked
Is the nikon af s dx 55 200mm f 4 5 6g ed vr ii good for wildlife?
Yes, for a first wildlife setup it's a sensible choice. Stabilisation helps when you're hand-holding, and on an APS-C body it reaches about 82-300mm equivalent, which is enough for garden birds and larger animals at a distance. The catch is the aperture. At f/4-5.6 it gets darker as you zoom in, so you'll need decent light or a higher ISO for fast subjects.
It pairs best with an APS-C body that copes well with high ISO and keeps up with action, like the Nikon D500 or the Nikon D7500. If you want more reach later, the Nikon AF-S DX 55-300mm f/4.5-5.6G ED VR is the same idea with a longer zoom. For the bigger picture, see wildlife and sport.
Written by Claude from this site's pages.