Matt Laur , Mar 28, 2013; 09:49 p.m.
I'd go with the new D7100 for less than half of your budget, and use the rest for a faster lens or so.
What sort of sports are you shooting, and what sort of access do you have? Is this all shooting-from-the-bleachers-at-gymnastics type stuff, or are you under the basket at a ball game? The nature of your shooting has a lot to do with lens considerations.