The top zoom lenses for your Nikon APS-C DSLR are listed below categorized by which lens provides the best value for money and the ideal choice without budget considerations.
AF-S DX NIKKOR 55-300mm f/4.5-5.6G ED VR -$299 to $399
A good telephoto option for Nikon DX cameras which can handle your long range photo taking requirement and also provide good value at $299.Not particularly good at taking low light shots and maybe a little slow to focus but for the price you are getting a decent lens.
AF-P DX NIKKOR 70-300mm f/4.5-6.3G ED VR – $399.95
The ideal option for DX cameras with sharp optics and fast autofocusing for capturing fast action at different focal lengths. This lens will give you good reach and it also comes with VR to offset camera shake to produce good photos but be sure to get the VR version of this lens (check for VR in the name) as the same is available without VR which cannot match the VR lens in performance.