Welcome to the forum!
Your camera body does not have a focusing motor to drive pre-AF-S lenses, so be sure that any lens you buy is designated AF-S, if you want auto-focus to be functional. If choosing a third-party lens, make sure it has its own focusing motor.
Then, look for the lens suitable for the distance at which you wish to work. Each Nikon micro/macro lens has a minimum focusing distance, at which the subject will be at 1:1 magnification on the sensor. (Some older Nikon lenses, and some third-party macro lenses, will be at 2:1, or another intermediate magnification.) A draw-back to a close working distance is that it can be difficult to light your subject, as the lens can cast a shadow.
I am not sure of the best working distance for jewelry, so cannot offer a specific recommendation, but when I photograph small items of evidence, I use a 100mm Canon macro lens. A shorter focal length might be fine for inanimate subjects, but I must also photograph living subjects, and the working distance of a 100mm macro lens can be close enough for discomfort.
I am unfamiliar with Nikons' Micro-Nikkor lenses, but would like to try both the 60mm AF-S 2.8G and the 200mm f/4D, eventually. I am participating in this thread to learn.
Notably, the 200mm f/4D Micro-Nikkor is not AF-S, so would only work on your D3000 if manually focused.