Focal Lengths: You often can get closer to the subject when shooting sports than when doing wildlife, so you don't need such long focal lengths. But fast lenses can be helpful for night action. A good, albeit pricey, starting sports lens is a 70-200mm ƒ/2.8 zoom. It lets you shoot at a shutter speed two to four times faster than a 70-200mm ƒ/4 or 70-300mm ƒ/4-5.6 zoom, which can help produce sharper action shots. (Image stabilization won't help stop action—stabilization just counters camera shake, not subject motion—but higher ISO settings will give you faster shutter speeds in a given light level.)
Nikon 70-200mm ƒ/2.8 G ED VR II.; Sigma 70-200mm ƒ/2.8 EX DG OS HSM
At some venues (especially non-professional ones), you can get close enough to use wider lenses, and doing so will provide a different (expanded) perspective. In good light, a superzoom can work; in lower light levels, a 24-70mm ƒ/2.8 can prove very useful. The superwide zoom of the landscape shooter (14-24mm, 16-35mm, etc.) will be less useful in most sports situations, unless you can acquire a field pass and know how to stay out of the way. If you can't get very close (as when shooting from the stands), a longer lens can be useful. Pro sports shooters often use the "big guns"—300mm ƒ/2.8, 400mm ƒ/2.8, 500mm ƒ/4, 600mm ƒ/4 and even 800mm ƒ/5.6—but these are very bulky and very costly. If your budget doesn't permit one of the big guns, one of the long wildlife zooms can do the job (although at a higher ISO setting to offset the slower maximum aperture): 70-300mm, 80-400mm, 100-400mm, 120-400mm, 150-500mm and 200-500mm.
Add A True Macro Lens
Tamron SP 90mm F/2.8 Di VC USD
Some superzooms are billed as "macro," but this generally just means that they'll focus closer than "non-macro" superzooms—down to maybe 20 inches for a reproduction ratio of 1:4 (1/4 life-size at the image plane). This is very handy for a lot of outdoor subjects, such as flowers, butterflies, building element details and the like, but it isn't really macro. Macro starts at 1:1—life-size at the image plane. True macro lenses will focus close enough to provide this life-size magnification. They're also optimized for such close range (they can better handle a flat closse-up subject). If you find that you're shooting a lot of detail shots, flowers and bugs, you might want to add a true macro lens to your outdoor lens kit.
Macro lenses come in three basic focal-length ranges: "normal," "short telephoto" and "telephoto." For a full-frame camera, that would be around 50mm, 100mm and 200mm. For an APS-C camera, about 30% shorter: 35mm, 70mm and 135mm or so. A longer macro lens produces its life-size magnification from farther away, handy when you don't want to get too close to a flighty or hazardous subject like a wasp, and the greater working distance also gives you more room to set up your lighting (most serious macro photography is done with a ring light or off-camera electronic flash). A shorter macro lens lets you shoot closer to the subject, which provides a more three-dimensional perspective.