Renting is a very good idea. The big thing you need here is versatility & a fast AF system in the lens. If choosing a longer lens like the Canon 100-400 vs others the limiter switch speeds things up when compared to a lens which travels the full range of it's focusing system before starting back in the other direction. I've shot the Sigma 80-400 OS, 50-500 non OS & the Canon 100-400 L IS & it clearly won the battle re AF speed / accuracy when shooting fast moving targets. I have also used the Canon 70-200 f2.8 L IS (ver 1) but it was a bit short on the long end but was more than up to the task. I haven't ever tried shooting action through a TC so can't comment on that.
EDITED to add
You also want to verify that whatever lens you think might fit your budget has an IS (VC, VR, OS) mode for panning. Some lenses need the stabilizer turned off for panning & if you don't do that the images will be soft.
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