First I will qualify my answer since I don't have a D5100. I don't use Auto ISO either. I always use the lowest ISO setting possible for the given subject and ambient conditions. The best settings (both shutter speed and ISO) is dependent on your subject, the focal length you are using, and the ambient conditions. 1/125th sec. is a reasonable minimum shutter speed for general photography but too slow for shooting sports or shooting at focal lengths longer than 100mm or so without VR.
The D5100 should have no problem producing clean images at ISO 1600 or even a little higher if you nail the exposure.
Auto ISO and Flash do not play well together. When you shoot using flash, you should always turn off Auto ISO and set the ISO manually. Good Luck and Enjoy your Nikons!