Best (cheapest) telephoto sports lens for a Nikon D90?

I just got a D90, but it only came with a 18-105 lens, and I plan on using it to take pictures of lacrosse games from the sidelines. I'll be using it outdoors during the day, and I need a lens, preferably a 70-300, but I'd settle for a 55-200. I'm on a super-budget, so I'm hoping for <300, and I'm only 17, so it won't be pro, just personal use. What could/should I get?