IMO a manual focus lens for sports is going to be a nightmare...especially with a sport like soccer or something. You would be better off with the 300 F4 and you can find a used/refurbished one under $1000.
I find manual focus as good, sometimes better than autofocus, for sports. You choose the shots you will take, you set them up with predetermined focus areas, you take. That area will always be 100% in focus, unlike in autofocus where you camera may miss because its autofocus isn't fast enough, or it focuses on an arm instead of a face or chest or something.
It takes more work, but honestly, unless you sports are very easy to track sports like car racing or bicycles, manual focus is just as good, if not better. The only thing is you will walk away with like 200 shots instead of 2000. Less deleting afterwards.
@OP - regarding the 300 f/4,5 lens, it IS a stiff lens. A lot of Nikon's older lenses were made with heavily damped focus rings for accuracy and so that when on a tripod, you wouldn't as easily bump the focus off. The 300 f/4,5 is a great lens and very cheap, but if you want slightly better compression feeling, the 2,8 is better. However, it is heavy. The f4,5 is great as you can hand hold it all day with no problem and get very clear shots. See if you can test both lenses side by side.