he is a national treasure and a master of his craft.

I feel much better using FX lenses on DX rather than the other way around. I purchased a 70-200 f4 with VR for my D500. The lens has been pretty well regarded by people like Thom Hogan. I paid 1k. (used) and feel it is a super value. Another option is a recent version of the 70-300 4.5-5.6 VR - you should be able to get this done for around 700 new and less used. A used nikkor 135mm manual focus is a terrific value in term of image quality but not so hot for sports. One of the great things about shooting Nikon is the lens system. You don't have to deal with the problems raised by putting dx on FX.

Good Luck and have fun,

Allen