If you could only have three lenses to shoot video AND general photography on FF cameras, (including sports, portraiture with or without flash, macro, etc.), which would you choose?
Since your question doesn't appear to limit the choice to those available...
A 17-40 IS USM that doesn't suffer from stupid amounts of field curvature or soft corners
A 24-105 IS USM that doesn't suffer from stupid amounts of field curvature at the wide end or soft corners at any focal length
A 70-300 IS USM that provides a sharp image and good focusing without weighing a ton.
(For mine, the 24-70 and 70-200 lenses don't offer enough flexibility in zoom range but do have IQ..)
Of course, if I could have only one, it'd be the 50-500/f1.4