Zoom for sports, there really are only 2 zooms worth considering;
1. AF-S 70-200/2.8VR I/II - VRI about $1500 used mint the VRII $2000-$2400 new and used. Not a great deal of difference between them, the VRII has Nano coat, VRII system giving a claimed extra stop of hand hold ability but the magnification at close focus distances on the VRII is lower than the VRI, also vignetting is reduced but not eliminated on the VRII, although the VRI was not that bad at f/2.8 and all but gone by f/4. For field sports, both of these esp on a FX body (D700 you have) will be too short and would be best used with teleconverters, just avoid the TC20EII, the 1.4, 1.7 and new TC20EIII are all fantastic with these 2 zooms.
2. AF-S 200-400/4 VRI/II - VRI about $4000-4600 mint used and the new VRII $6300+ new. The new version has VRII so an extra stop as above with the 70-200 of hand hold ability and it is sharper at the long end than the VRI. The VRI is no slouch though and the zoom range on both of these is very handy for covering both indoor and outdoor sports. Either can be used with a teleconverter to get more reach, but as the lens is already an f/4 wide open, the 1.4x TC is about all that is going to be really useful for sports and AF will be slower than without the TC. You can use the 1.7xTC but in anything but good sunlight, AF will not work very quickly and sometimes not at all. This is a large beast, and unless you have good arms, hand holding it for more than a few shots will probably prove difficult, so a monopod/gimbal will probably be required.
You can opt for 3rd party Sigma's, Tokina's, Tamron's etc which can be had much cheaper, however they are not in the same class as the Nikkor lenses.
When it comes to glass, you can rely on the theory of getting what you pay for.