I think you need to explore some options to see what's most comfortable for you. A shoulder bag is certainly a good suggestion. They also sell belts that you can attach lens cases to.
Two of your lenses are on the longer, heavier side (300, 70-200). A belt rig could work if you put one on each hip.
You'll have to decide what you're comfortable with. What provides the accessibility you're looking for without impeding your movement.
Whichever system you decide on make sure it includes camera retention. Example black rapids sports breathe or wrist strap. You often need two hands when making lens changes. For mounting, removing or for removing, replacing lens caps. Sling bags are also very popular.
I typically carry two lenses for day excursions when I travel. I do my best to anticipate what I'm going to see and shoot that day. Then make choices. Backpacks are nice to, but lens changes are not seamless, especially if you're on the move. Hopefully you can figure out what works best for you. 😉
I agree with Rick that with the heavier lenses, I would use a belt based carrier to keep the weight lower. And definitely pay attention to something that will keep the camera body and lens secure during fast change operations while you are shooting sports because one slight misstep and things get expensive!
IF you later decide to go to a dual body setup, I highly recommend the Sun Sniper Rotoball double harness. I tried several and this one is the best I have used and I have had it for about four years now. It easily splits into two separate harnesses via releasing a wide velcro joining strap which is great when you are using large body/lens combos that won't easily fit together in the same travel case. I typically have an EF 400 f2.8, 300 f2.8 or 200-400 f4 1.4X integrated extender on one side and a 70-200 f2.8 on the other; both paired with 1DX III bodies and it handles them comfortably during long sports events.
It has provisions for attaching a third body that hangs near the center of your chest and I have used that on rare occasion but it is not comfortable running down the sidelines with a third camera in that position; the side mounts work very well and have shock absorbers built into their straps.
The primary attachment is to the camera body or tripod foot via their "rotaball" swivel but there is an integrated safety strap in case you didn't properly secure the swivel thread into the tripod foot. I haven't ever tested it but one of the local media guys did with a 1DX II and EF 300 f2.8 at a basketball game and the safety strap did its job but I think he lost a couple of years off his life when he felt that expensive body and lens appear to head to the floor before the safety strap stopped the fall 🙂
Rodger
