Hey folks!
I'm getting back into the hobby this summer and am putting together a kit. I plan to do wildlife photography while hiking
The place to start is, what lens do you want to use? For wildlife photography, a 500mm final length will bring the subject closer. I do not recommend going shorter. 600mm is as long as I'd recommend a beginning wildlife shooter go.
The next question is how to address the low light issue. There are two approaches: lens aperture and sensor size. I'll recommend not going any slower than f/5.6 in aperture. That eliminates the 150-600 consumer zooms and there will be plenty of folks who will argue the other side of this. From personal experience as a longtime Nikkor 200-500mm, f/5.6 owner, the biggest limitation of the lens is that it's not an f/4. There's just no way I'd go to an f/6.3 maximum aperture optic. Again, just one person's opinion. As with all such things, YMMV.
One of the advantages of shooting full-frame. Is that the sensor captures as larger volume of light in comparison with an APS-C or smaller sensor body at the same exposure settings. There is a caveat to this: you will only realize that advantage, if you're not cropping the finished image any smaller than an angle of view larger than an APS-C sensor would deliver under the same conditions.
Suppose two photographers are sharing a hide. One is shooting full-frame, one APS-C and both are using the same 500mm focal length at the same f/5.6 aperture. An elk wanders by. Both photographers make exposures at the same shutter speed. The APS-C shooter fills the frame. The full-frame shooter ends up cropping to an angle of view matching that of the uncropped APS-C image.
In this scenario both images are made using the same volume of light. Both images have the same noise and depth of field. The light-gathering advantage of the larger sensor is negated by the need to crop. So the core question becomes, how often will you crop to an APS-C or smaller angle of view, if shooting with full-frame?
Are you in an area where hunting is prohibited, where the animals do not see humans as a threat? If so, there's a reasonable chance you'll be filling the frame of a 35mm equivalent camera. If you live someplace where animals are hunted and large mammals keep a healthy distance from humans, a full-frame camera probably offers zero advantage in comparison with APS-C. In fact, unless you go with a high megapixel body, full-frame could be a genuine disadvantage.
If it's my nickel, the place to start is the Nikon D500 and Nikkor 500mm f/5.6E PF. This would be a relatively small but highly capable kit. If you're concerned about low light, the only way around that would be to pair the camera with an exotic prime...a 500mm f/4 or 400mm f/2.8. They're large, heavy and pricey, but they're among the absolute best in wildlife optics. If the 500 PF is more than you want to pay, the 200-500 is a lower cost option.
Best of luck with your decision.