SIgma has an affordable 70-300mm lens with an APO designation,and it's dewcent according to what I have actually seen from it--but make 100% sure it is the APO model of 70-300 from Sigma; the non-APO model is lower quality.
The 70-300 G is/was a low-cost, ultra lightweight $125 lens. I own one. It is discontinued as far as I know. After it Nikon made a 70-300 model commonly referred to as the ED model, which was as I recall an f/4~5.6 model. That was a $599 or so lens. Below the ED was the 70-300 f/4.5~5.6, as I recall, and that was a $329 model if my memory serves me correctly.
A couple of years ago, Nikon SIGNIFICANTLY upgraded the optics, and put VR into its highest-end 70-300mm lens, which is the new 70-300 f/4.5~5.6 VR-G; a slower maximum aperture than the older 70300 ED glass model, BUT better optics and VR--capable of being used on higher-resolution cameras.
Thom Hogan's web site and Ken Rockwell's website might be of help; I'm pretty familiar with a lot of Nikon stuff, but I have not kept up on the 70-300 class of lens for many,many years--hence my use of words like "as I recall" and "if my memory serves".