A heavier telephoto lens can be an advantage, because more weight makes it easier to avoid camera-shake at long focal lengths, especially when you're panning.
A good-quality optical stabilisation system makes for much greater consistency when you're attempting to get sharp handheld telephoto shots.
Autofocus speed tends to decrease at the long end of the zoom range in telephoto lenses. This is most noticeable in 70-300mm lenses.
Ultrasonic autofocus systems are generally much quieter than the more basic electric motors fitted to some lenses.
On the move
Faster, ring-type ultrasonic autofocus, as fitted to the Nikon 70-300mm VR and Tamron 70-300mm VC USD, is better for tracking fast-moving subjects.
Time to downsize
Choosing a 50-200mm or 55-200mm lens specifically designed for DX-format Nikons saves on size and weight while still enabling a generous 300mm effective telephoto focal length.
Mind the gap?
There's no need to worry about the gap in focal length between an 18-55mm kit lens and a 70-300mm telephoto zoom. In practice, this really isn't a problem.
In the hood
Fitting the lens hood supplied with a telephoto lens not only guards against ghosting and flare but also protects the front element from knocks and scrapes.
You often need to shoot at maximum aperture to maintain sufficiently fast shutter speeds, especially at long zoom settings. Therefore, good optical performance with the lens 'wide open' is key.
Mix and match
Lenses in which the front element doesn't rotate during focusing are much easier to use with rotation-sensitive filters such as circular polarising or graduated filters.