Keep in mind that this is a PRO LEVEL lens, expensive, heavy/bulky!!!
The benefits of getting "good FAST glass" are many...this lens is primarily for SPORTS photography. Also serves well -outstanding is more like it- as a portrait lens and being able to shoot in "low light" situations without flash/tripod.
You can consider the Nikon VR 18-200mm for about $1K less...you can get an ALL AROUND lens that will not be heavy and bulky for "everyday use".Sports (fast moving subjects) will be an issue with this lens. This lens is also compatible with your D60.
This lens (70-200 2.8 VR) has an internal motor in the lens that will work with your camera (will allow auto-focus to work). This is from the AF-S (Auto Focus Silent wave motor)
IF- is for Internal focus and all it means is that the lens will NOT EXTEND when zooming in on a subject (the 18-200 will).
The D60 also supports VR which is "Vibration Reduction" an internal lens (element) that moves up and down ( powered by cameras internal battery) to reduce the effects of camera shake (in theory better pictures without a tripod). VR works well but it is not FULL PROOF. Make sure to read the owners manual and understand how VR works and its limitations.
In my camera VR uses a LOT OF JUICE! So keep that in mind as you might need to purchase an additional battery. (IMHO/FWIW: there should always be a second battery available)
EDIT: IF you do go with the 70-200 2.8 make sure you learn to use/hold the camera by the "lens" and not the camera! This lens can put some strain -mounting plate camera/lens-on even "pro-level" cameras so be cautious. There should be no problems as long as you learn to walk/hold the camera by the lens. On most (I think it is all of them but do not quote me on this) Dx0 series Nikon cameras the mounting surface of the metal "ring" is plastic!
I would forget the VR (unless shooting sports in LOW light) and go for the 80-200mm f/2.8D ED. This lens is as sharp, if not sharper, and about 1/2 the price. I think you can find it as low as $700 on amazon and probably cheaper elsewhere. Though... VR is a nice touch, is it worth an extra ~$1,000?