The 24-70 f2.8L II and the 70-200 f2.8L IS II are my workhorses. For anything indoor -- sports, events, portraits -- these two lenses meet just about any need. They top my Four Lenses I can't Live Without list.
The 100-400 f4.5-5.6L IS II and the 40 f2.8 pancake round out this list. The 100-400 is a recent acquisition, just in time for last summer's sporting events. When there's light, it's easy -- very easy -- to like this lens. It's fantastic for sports, focuses very quickly, and can still provide creamy backgrounds. For outdoor work, I generally leave the 70-200 home and bring this lens (unless I'm shooting portraits) and either the 24-70 or the 40.
The 40 is my travel light lens, for obvious reasons. Many times I only need the long zoom, but always bring the 40 just in case I need something wider. This lens is also great for more casual events like burgers with the team, where you want something less obtrusive.
Of these four lenses the 70-200 is my most used, by far. This lens is particularly great for candids and portraits.
If funds allow, I would certainly recommend starting with the 24-70 and the 70-200, then adding the 40 and the 100-400. For what it's worth, I considered tele-converters with the 70-200, but opted for 100-400 for several reasons. When compared to 70-200 on a 2X converter, the 100-400 has better IQ, potentially better focus performance, and the 100-400 range is more useful than 140-400. On paper, the tele-converter route is more versatile. In practice, this means more lens and converter swapping -- more wasted time, potentially more lost shots, and a greater risk of getting dust on the sensor.
Last thought. I most often shoot with two bodies, one with a short zoom and one with a long zoom. There are other great lenses to consider. I like the 24-105 f4L IS and the 35 f2.0 IS. These lenses give me the option to play with controlled motion blur using slow shutter speeds. The 35 is also great for low light and smaller DOF. I may add a fast 50 and/or a fast 85 in the future. But, I consider these to be specially lenses for more specific types of shots. If shooting an event where getting the shot is critical, the 24-70 and 70-200 on two bodies can't be beat. They're great for low light, cover a wide focal range, and no time is lost in changing lenses.