You could also check out the used market for an older manual focus lens and go old school on it. Makes it tougher on wildlife if they are moving, but can be done with some practice. Some of the older Nikon manual lenses are very sharp and render great color without breaking the bank for VR, autofocus, auto aperture, etc.... Check out Adorama, B&H, and KEH. I have bought used equipment from all of them and have been impressed with every single purchase so far. There are other places that sell used equipment, but those are the only 3 I have personally bought from. Just remember that Ai lenses will fit, but the older non-Ai will NOT. You can tell by those little "rabbit ears" by the aperture markings. Non-Ai have solid "ears" while the Ai ones have holes in the ears (
This site shows and explains MUCH better than I ever could).
Adorama has a
Sigma "Bigma" right now just a touch over your $500 limit ($549) that is 50-500mm with autofocus that will work on the D3200. I used to have a big problem with 3rd party lenses, but have found that for now the Sigma EX line work exceptionally well (reports that they will NOT work on the new breed of Nikon bodies should be taken into consideration as well.)