Hmmm long distance.
I suggest you look at a Micro 4/3 camera; either Olympus or Panasonic.
With the 2x crop factor a 75-300mm lens is a 3-12x lens, similar to a 150-600mm lens on a FF camera. Same magnification in a smaller/lighter package.
There is a common fallacy about the full-frame lens "equivalence" calculated from the crop factor, which itself derives from the sensor size. The equivalence is correct when you want to match the same field of view. But what most wildlife photographers want is to maximize the number of pixels for a subject that doesn't come close to filling the frame.
You can quadruple the number of pixels on a subject by doubling the focal length. Or you can quadruple the pixels by halving the pixel pitch. The sensor size (and crop factor) is irrelevant.
The common wisdom is that if I have a full frame camera and a 2x crop camera, I would need a 200mm lens on the former to match a 100mm lens on the latter. However, if the pixel pitch of the two cameras is the same, I could use the same lens on both to capture a distant subject. As long as the subject fits entirely within the field of view of the smaller sensor, a crop of the subject from both cameras will be identical (for nitpickers: same lens, same focal length, same sensor electronics--same everything except for the sensor size). The 2x crop camera will
not gain a magical 2x zoom benefit.
I use the term "zoom factor" for the ratio of the pixel pitch of two cameras. Unlike crop factor, which is always a comparison to a full-frame sensor, there is no standard to compare against. You can only look at the "zoom factor" difference of two specific cameras. As an interesting aside, if (and only if) two cameras have the same number of pixels, then the "zoom factor" equals the crop factor.
If you square the crop factor and multiply it times the total pixels on a sensor, you get the number of pixels needed to have a zoom factor of 1 when compared to a full-frame camera. So a 2x crop 24 MP camera and a 96 MP full-frame have the same pixel pitch. Since many crop cameras have a pixel count close to 24 MP and few full-frame cameras approach 96 MP, people tend to believe that the crop factor is the source of magnification.
For bridge cameras, the manufacturers love to push this idea, so you'll hear (and I do) amateur bird photographers talk about how they have the equivalent of a 2000mm lens on their Nikon P900. Well, maybe yes, maybe no--it depends on what camera they are comparing against.
As far as advice on what equipment to get, I think it's been covered pretty well. The Sigma Contemporary 150-600mm is supposed to be a pretty good lens. You can extend the range by getting their 1.4x extender. Crop cameras tend to be cheaper and have a smaller pixel pitch. I don't know about Nikons, but the Canon 80D is about $850 and a Sigma C runs around the same, so that fits well within your $3,000 budget, even if you add the extender.