How to judge the minimum shutter speed on a DX camera?

I have a Nikon d200. The color is amazing, yet I seem to be having a bit of a problem at low light. As an old film shooter, I learn a ground rule, your lowest shutter speed should match the focal length of your lens, for example, a 50mm f1.8 lens should use a minimum of a 1/50th shutter speed. However, the DX frame treats a 50 mm like it was a 75mm. Consequently, should the minimum speed used (again a rule of thumb) be 1/50 or 1/75? Any references?

Yes, include the crop factor in the equation.

Put the camera on a tripod. The shutter speed = focal length is for handholding. (AFAIK, perhaps there's some other consideration that I'm not aware of.)

I think the shutter speed rule will need to account for the crop as the crop is actually a magnification. It also depends a lot on what you are shooting. A portrait does not have to be quite as sharp as a product shot. In addition, remember that nothing is sharp at 300%!