A great 'budget' sports lens for well lit venues and sunny days is the 70-200 f/4 L. Using a battery grip will give you power peace of mind while out there for hours on end and a good handhold while shooting in uneven terrain.
Get a sturdy monopod and learn to pan. Don't fall into a spray and pray or chimp trap. Start with cycling as snow and shadows can be tough to work with in PP for WB and exposure concerns. Want to study a great cycling photographer? Check out Mark Johnson at Ironstring. He just did a book on Garmin called 'Argyle Armada' with amazing shots.  Get your Servo skills down. Use the custom functions and back button for AE and AF. It's fun shooting races but don't expect to have as many keepers as you'd like, you need to focus on expression and angles. You'll also throw out a lot of helmet and shots from behind. This is why panning is important. I shoot cyclocross races and that allows many unique perspectives and angle opportunities.

Good luck!