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For your requirements I don't think a 70-200 would be long enough. The player would have to be pretty close to the side line if you want a full frame body shot at 200mm. Ideally you'd want a 300 or 400mm lens to ensure you can capture decent shots of players anywhere on the pitch.

The best zoom lens for the job is the Canon EF 100-400mm f4.5-5.6L IS USM, but it's slightly above your price range. You could consider the Canon EF 70-300mm f4-5.6 IS USM. Not as good optically but still decent and great value for money. There is also a Sigma 120-400mm f/4.5-5.6 DG OS HSM available, but I haven't read up on this lens so you'd have to do some research.

Alternatively you could go down the fast 70-200mm + 1.4x tele converter route, which would give you an effective 98-280mm lens while sacrificing 1 stop of aperture. Both Tamron and Sigma offer 70-200mm f2.8 lenses that fall within your price range. The Tamron is sharper but the Sigma has HSM and therefore is faster focusing, so take your pick. However, neither has IS (the IS versions are a lot more expensive).

Finally the Canon EF 70-200mm f4L IS USM is a great lens but with a tele extender it would be rather slow for sports (f5.6) and without one it doesn't quite have enough reach.

I would personally recommend the Canon 100-400 if you can get hold of one at a decent price, or the Canon 70-300 which has everything you want at the cost of some minor loss of sharpness at 300mm.