Compatibility comes first
The lens mount must match your camera system or a tested adapter. The manufacturer's name in the title is not proof of compatibility. Find the exact version of the model, as similar names can refer to lenses for different cameras.
Choose the focal length and aperture for the kind of photography you do. A wider angle helps indoors, a telephoto lens with distant subjects. Also consider the weight, minimum focusing distance and whether the lens covers your camera's sensor format.
Condition of the optics
Check what the description says about scratches, haze, fungus and mechanical damage. A little dust and serious optical damage are not the same, but the effect on images can't be judged reliably from an outside photo. Test shots and a specific test result help.
Autofocus, stabilisation and aperture should each be checked if the lens has them. Uneven movement of the focus or zoom ring may need servicing. Look especially closely for impact marks near the mount.
What's included and choosing
Find out whether the front and rear caps, lens hood and other accessories are included. Compare identical model versions and their condition. A lower price won't fix incompatibility, so before you bid make sure the lens fits your camera and the features you need.