Got there in the end then!
Look at the Nikon 70-300 mm over the 55-300 mm lens though. Much less distortion.
If you are recommending lenses the 70-200 is likely the best mid-range zoom ever made period. In fact all version of this lens going way back to the pre-digital era were so good that it gave reason to buy a Nikon body, just so the you could use this lens. Used versions are less expensive.
I've used the 70-300 and it's not great, some blur and some purple fringe.
One thing to think about is with wildlife you are best to shoot in early morning when the sun is very low or in the evening when the sun is low. But you will have more wildlife to shoot in the early mornings. No mater what, with each 1 stop faster lens you can reduce ISO by 1/2. A couple stops make a big difference in noise and quality.
With low light and 200mm lens the fast f/2.8 f-stop helps a lot. Older examples of this lens sell for as low as $650. And like I said this lens is the reason many people own Nikon gear. (Although in resent years the Canon equivalent is as good)
I'd spend on a well used 70-200 f/2.8 before I paid the same for a new 18-1xx telephoto zoom.