Gotta give another vote to the D7200. Incredibly capable camera for around $500. It can shoot fast enough for most wildlife (assuming your glass is fast enough) and is just easy to use.
Yellowstone is a tough place to shoot because half the stuff you are right on top of and are huge (old faithful, grand prismatic, etc) and then the animals can be forever away.
I would go-
D7200
Nikon 18-105
Sigma sport 150-600. (Although I recently picked up the Nikon 200-500, and it is a higher quality lens, for marginally more money)
And if you have 300 left over, grab a tokina 11-16. F2.8 will let you do all the low light stuff you want, and take pictures that are very close to as, “wide” as you can see with your eyes. The 18MM should be good on the crop sensor. The 24-120 is a fantastic choice, but sometimes it feels just a hair too long at 24mm for walking around.
Be sure to grab fast enough memory cards for whatever body you end up with!
Edit- I don’t know what your photography background is, but buying used gear from Adorama or B&H is a super easy way to get better gear at a way lower cost.