70–200mm f/2.8
$$$$f/2.8 is playable indoor light and a usable background melt on a field. 70–200 is the range you can actually stand on a sideline with. A 70–200 f/4 is lighter and cheaper if you only shoot Saturday morning sun.
What to look for: Constant f/2.8, optical stabilization, a tripod/monopod foot. Third-party (Tamron 70–180, Sigma 70–200) is the honest value.
Skip it if: you only shoot outdoor sports in good light. A 70–200 f/4 or a 70–300 is a lot of the way there for less money.