70-200 f/2.8 IS II is a great lens now and will be 30-40 years from now. if it's too much money get VI or even Canon IS version. But I'd go sigma before I went f4. At least for sports 70-200 f/2.8 is the best lens to have. Add a 1.4X converter and you are close to 300mm.
Of course you should have other lenses. From fisheye to 800mm there are uses for them all in a sports environment. Which is the 2nd best lens? Definitly a mid range zoom like the 24-70/105. A 300/400mm f2.8 would also be nice but is a bit pricy.
Oh and I recommend a monopod with the 70-200 f2.8, it can get very heavy over time.