Hello
1) Nikkor 80-200mm f/2.8 AF-S ED IF.
Pros: fine lens, sharp wide open, nice colours, well built, fast AF, AF lock buttons on the lens barrel.
Cons: heavy, doesn't work well with TC, known first generation AF-S motor issues.
If you can find a clean copy with minimal internal dust, reasonable price and AF motor is silent, it is a good buy. I have a copy of the lens in grey white. I have been using it since early 2000 with my F5, no problems so far.
2) No comments on the Nikkor 80-200mm f/2.8 AF-D ED IF and Sigma 70-200mm. Never owned either of them. Check on line there are plenty of reviews on these two lens.