two words… long and fast.

long… how far away will you be from the action vs how close do you need to get with the lens? this dictates the length you need. longer lenses definitely require image stabilization.

fast… large aperture for low light, low iso and fast shutter speeds to stop the action without blur. fast reliable auto focus that can ‘track’ your subject and maintain focus.

fixed focal lengths are generally too limiting for sporting events so go for the zoom. don’t expect one lens to do everything you need. remember to bring extra batteries, extra memory cards and a solid but lightweight tripod or monopod.

If you can hire a 400 mm f/2.8 or 600 mm f/4, you will be happier with the results. You will also want at least a monopod.

The 100-400 mm lens is a good one, although at 400 mm its aperture is f/5.6

I think the big guns that fhotoace mentioned are great.

I do have the 100-400 mm lens but have not used it for that sort of sport, but can show you two photos that you can view in full size here:
outdoor at 320 mm
indoor at 365 mm at 1/60 of a second (!) As you can see the IS works quite well here.

It focuses very quickly–and without a sound. The lens is heavy. I think it’s almost 5 pounds or so?

The zoom ring, if there is such a thing, is kinda weird. It’s a push-pull design, but it has a control that you can actually lock it into place, or completely make it “loose”. See here: for review.

Hope this info is useful for your decision.