I shoot a D750, and even though my main gig is portraits, I do some "non-pro" sports and wildlife as well.
For sports, I find the D750 is a great camera for the non-pro. Frame rate is not 11/second, but it shoots fast enough for me and did not cost $6k. You could get a used D3(S), but then you're down to 12MP vs 24MP. Megapixels really aren't a huge deal with me, but when you capture a perfectly clear shot of say a deer, it's nice to be able to crop tighter in post and still maintain that clarity. 12MP may still be sufficient, but 24MP sure can't hurt. And speaking of wildlife photography, the AF of the D750 is excellent. Ive shot the D90, D610 and D750. The D90 is good. The D610 is better, and in my opinion about equal to the D750 until conditions get really dark. That's where the D750 takes over. The D7200 AF might be just as good, but I find often my better opportunities for wildlife come at low-light times of day, especially after the sun has gone down. For that you may have to shoot at higher ISOs, and I have to think the full frame sensor would be better than the cropped sensor.