DSLR and Lens to buy for wildlife photography: Suggestions Expected from Experts?

Have you considered Nikon's 200-500mm f/5.6E ED VR Lens. One main benefit is that this lens has a constant f/5.6 aperture while the Tamron & Sigma equivalents have variable apertures from f/5.6~6.3.

None of these lenses are what I'd call cheap, so maybe renting the Nikon and Tamron would be a wise decision? Not only in terms of pure image quality, but in handling and focusing speed.

I see you chosen the full-frame D750, which for what I hear and have seen, is a pretty darn good camera. But what about going with an APS-C format D500 instead? You'd get the 1.5x crop factor which is going to be a huge advantage for you over any slight image quality that a full-frame sensor will provide. The D500 has 3x more focusing points, and shoots at 10fps vs just 6.5 on the D750. If you were to be shooting landscapes instead of wildlife, I'd definitely go FF over APS-C, but for wildlife, your needs are completely different and I think APS-C provides an advantage here.

Canon DSLR with L Series lenses have been more than good enough for famous wildlife magazines for many years.

I would go with the Nikon D500 (crop factor gives a bit of magnification), although, the D750 is also a good body.

For a lens, Nikkor 200-500mm at f/5.6 over the whole zoom range. The 200-500 is a game changer in affordable telephoto lenses due to the image quality at 500mm. With a crop sensor camera like the D500, the 500mm end of the lens has an equivalent field of view of a 750mm focal length.

The Tamron lens maximum aperture changes with focal length, thus, at 600mm the max aperture is f/6.3, 1/3 stops off from the Nikon. Reviews on the Tamron lens appear to be quite favorable. If you can visit a store, try out both lenses and see how they perform.

I think you are on a good track,

but an even better one would lead to Pentax.