You asked
Best telephoto lens for the nikon d3300?
For the D3300, I'd start with the Nikon AF-S 70-200mm f/2.8G ED VR II. It frames like 105-300mm on this camera, it's fast enough for indoor sport and portraits, and its VR matters because the D3300 has no stabilisation in the body.
If you need more reach for birds and wildlife, the Nikon AF-S 200-500mm f/5.6E ED VR gives you roughly 300-750mm equivalent. It's slower at the long end, so you'll want good light.
For fast reach with a bigger budget and bigger bag, the Sigma 120-300mm f/2.8 DG OS HSM Sports is the serious option. It's heavy, though.
If you want something lighter and cheaper, the Nikon AF-S 70-200mm f/4G ED VR covers the same range with less weight.
For more on how to pick, see wildlife and sport.
Written by Claude from this site's pages.