I am late to the party and it sounds like there is some "budget creep" but that is a good thing with what you are trying to do. 🙂
Is your goal to cover the entire court with a single lens from your position in the end court? If so, a 100-400 is too long for covering the near basket area with a full frame 6 series and way too long with an APS C 7 series sensor.
For HS basketball, I use three bodies and three lenses with 1DX III bodies and 24-70 f2.8, 70-200 f2.8, and 300 f2.8 to cover the court from one location. Any telephoto longer than 300 won't be needed on a full frame sensor and around 200 is all you need with a "crop sensor" body.
Even with modern gear, f4 is about the limit for good photos unless you are shooting D1 college or better because typical gym lighting is decent but not great. Increased noise with higher ISO is part of the issue but ALL cameras (mirrorless and DSLR) will focus a little slower in low light with narrow maximum aperture lenses. For a couple of HS gyms in the area I found it best to use EF 85 f1.8 and EF 200 f2 lenses because the light level was bad enough that it was better to "zoom" with my feet than use my usual gear setup. So try to avoid anything "worse" than f4 in the range you will be using if you use a variable aperture zoom.
If you are doing a single lens you will need at least 50mm at the wide end (say around 30mm with an APS C sensor) and at least 200 at the tele end when using a full frame body. If you can keep the ISO reasonable, you can always crop the image but there is no way to add back what you can't fit within the frame at the point of capture and at the speed of basketball you have to leave some margin of error on the edges most of the time.
Below are some photos to give you an idea of what various lens focal lengths will provide while shooting from the floor just behind the basket. The first is with a 24-70 2.8 @ 28mm, the second is with the same lens but @ 70mm, the third with a 70-200 f2.8 @ 200, and the last with a 300 f2.8 prime. Most of your shots of ball handling near the goal will be within 70mm so you really don't want a lens that starts at 100 unless you are willing to back up to the wall which tends to limit your mobility.
Rodger
You are welcome! And I look forward to seeing what you capture!
Please always be on alert because a lot of the action doesn't stop at the lines. I captured this shot while sliding to the side as the player crashed into the back padded wall next to me. Two games later, a student photographer for the opposing school got trampled when she was checking her last image captured instead of paying attention to three players crashing the board and ending up spread across the run out area-fortunately the only injury was her camera lens separated into two pieces but she was okay. Sports photography is like driving, you can't let something like your LCD display distract you from what is going on around you.
Rodger
