> Sports would include cross country (could use either lens), baseball and basketball (might prefer 70-200), and indoor cheer competitions (definitely 70-200).
Cross country will be fine with any of the lenses that reach. Baseball is kind of short at 200mm - I shoot a lot of baseball and often go as long as 500mm even on DX. Even from the camera well, 200mm is kind of short. Basketball: indoors? I don't do that, but I routinely hear that it's very challenging from a lighting perspective. Most seem to be shooting with 50/f1.8 or 85/f1.8 or similar. Indoor cheer competitions seem to be a low-light thing too. Depending on how close you can get, that seems uncomfortably low light for an f/4 lens, let alone an f/5.6.
> I used the 24-105 almost exclusively on the 5dmk3. ... I thought the 24 was just on the edge of not being wide enough on FX at times.
Then 24 on DX definitely won't be wide enough. You'll need to add something wider to the 24-120. I personally got great results from a Sigma 10-20, but if you're after maximum IQ the Sigma 8-16 is the one to have. And clearly you won't need anything wider! 12mm on FX or 8mm on DX is just insanely wide.
I think you're better off with 8-16, 24-120/f4, 70-200/f4. Although the 70-300 has more range, I think it's dangerously slow at the long end for much of what you want to do. Unfortunately that will put you with three lenses that are either bulkier or heavier than perhaps is minimally required, but between the range and quality requirements, that's where I end up.
_____ Brian... a bicoastal Nikonian and Team Member
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