I think you should be looking at the various photo forums for used lenses. I doubt you could buy even one "L-series" telephoto for you budget, let alone al three lenses. Sports and Wildlife are the single most expensive subjects you can think of especially Wildlife.
You might be able to find a used 70-200 f/2.8 for about $750 if you hunt around.
One of the advantages of the Nikon line is that people on a tight budget can buy Lenses made back in the 1970's that will fit the newest bodies. canon changed their lens mount some time ago and obsolited their older lens. Nikon found a way to do autofocus without a lens mouint change as so even 40+ year old lenses still mount on the new D200 DSLR
As an example I have a 135mm f/2.8 lens I'd be happy to sell for $85. An outstanding portrain lens that I will NOT sell is the Nikor 100mm f/2.5 (
http://www.kenrockwell.com/nikon/105f25.htm) that sells for just over $100 on the used market. There were no consummer grade lenses back then they were all heavy with solid metel. No plastic mounts or the like. They typically outlast their owners. As for quality look to any 60's or 70's issue of National Geographic for example photos.