You have received some good replies here. I would encourage you to recognize that the D500 is an outstanding camera that will do a great job for you far beyond the bounds of wildlife photography. Be careful not to limit yourself when you are selecting lenses. I do not photograph wildlife as one of my primary genres, but have two of these cameras that get extensive use alongside my full frame bodies.

There are two guidelines to keep in mind as you select your lenses. The first is that any lens you own or buy will give better results on your D500 than on just about any other camera...certainly any other DX body. The second is that the D500 is completely able to take full advantage of any great lens you put on it. With latest firmware, it is the Nikon DSLR that is fully compatible with the longest list of Nikkor lenses.

I endorse the suggestions you have already received for the 17-55 mm f2.8 DX zoom as your primary "normal" lens. It is a fully professional grade lens that delivers outstanding image rendition. Sometimes I feel that it is better than the 24 - 70mm f2.8 to which it provides equivalent full frame field of view.

I can also second the recommendations for the 200 - 500mm f5.6. It's not built to quite the same standards of ruggedness and durability as some other similar zooms, but it is optically excellent and comes at a great price. If you ever ended up having to replace it, you'd still be financially ahead of a lot of other options.

I cannot endorse the 16-80mm zoom. It is sold as an f2.8-f4, but ends up being f4 over almost all of its zoom range. Because of that, and because it's really pretty average (in my opinion), I feel that it is pretty severely overpriced, even on the used market.

When I need a little extra versatility, I've been using a 24-120mm f4 G zoom that I bought used for $425 at my local camera store. This is the lens that the 16-80 is intended to emulate. On the D500, it covers a full frame equivalent of 35-180mm, which I find very useful. I'm not sure it renders images that are as good as the 17-55, but it is very good. I've taken some images with it that did pretty well in contests.

You have a lot of good choices available to you. I'd suggest not getting in too big a hurry and taking time to look carefully.

queencitysanta has a good starting list. Shooting wildlife and landcape I'd get the 70-200mm last. The 24-70mm will cover much of what you need, but since it's on a crop sensor camera you DO need something to cover the lower ranges. I don't think 10-18 is wide enough. I prefer a 10-24mm because I DO use that 24mm selection for landscape on my crop D7000 quite a bit. Tamron makes one that is a second version that is supposed to be excellent. I have the first and have enjoyed it. Nikon makes one also. I have a friend who uses the Sigma 150-600mm Contemporary on safaris and takes excellent photos with it. He previously used the Sigma 50-500 to the same effect but wanted more range. You could pick up a Bigma (50-500) used for a song, I'll bet.