The 100 - 400mm is a versatile lens but personally I don't like the variable apperture, and it can be a bit of a dust pump, though that should be less of an issue with self cleaning sensors. It was a real pain with my old 30D, but that always seemed to be a dust magnet.
When I supplemeted mine with a 70 - 200 f2.8 that soon became my go to lens, so much so that the 100 - 400mm soon got sold. Add a 1.4x teleconverter when a bit of extra reach is needed and it covers pretty much everywhere on field. The advantage of a full frame sensor is that you can crop pretty hard when you want to.
If I'm concentrating on a tape player I might switch to the 24-105mm for the closer minimum focus distance if the sideline is tight, or my 17-40mm for wide shots, pit crew etc.
That's the basic kit, I may use a prime sometimes, the 135mm makes an excellent candid portrait, I love my 40mm pancake as a walk around and for composite images. I also have used the 8-15mm and there is a hole in my bag for that and a 300mm prime.