Choosing a Tele 80-200/120-400?

I'm constant reader at DP, and this is a great source for some really good info. I have got a D600 few weeks ago, and a 50 1.4d to go along. To get some decent range, I was looking for a good IQ lens. In a few weeks I might be attending a Formula 1 gp, and so part of the reason for this purchase is that as well. However, I want to get a general purpose decent range lens. My plan after this lens would be to get a 24-70 2.8 sometime next year, and I'll keep this for tele for quite some time, hence this thread

My budget is limited to ~ $1k and so I have limited choices. After reading for a bit, I have come down to either the Sigma 120-400 or the Nikon 80-200. I was considering the 70-300 vr but it seems on the long end the lens softens a bit, I'd like to keep the IQ as good as a possible and so I have increased my budget. Another consideration could also be the Sigma 150-500, but then I think it might not be fast enough to get a f1 car, but thats just an impression I have got reading about. I'm open to other lenses too as long as I can find them around that range, perhaps a $100 over as well. I'd appreciate all your input!