Sports would be water sports, I.e, surfing etc, rugby which would be from a spectator stand so maybe 20-50 metres. The main use would be the wildlife and landscapes, so Birds, big Cats, deer, and some african wild animals (in the summer) I can spend around $500-600 on each lens, and yes one at a time.
With further reading, the Canon EF 70-300mm f/4-5.6 IS USM seems to be a favoured lens, with people using it for a similar purpose to my shots.
Thank you.