Nikon 50mm f/1.8D AF OR Nikon 50mm f/1.8G AF-S?

I'm the owner of a Nikon D5100.
I'm a dancer, looking for a lens that captures fast actions shots for my shows, and that can work great outdoors and in low-light settings for my theatere performances, where flash is not allowed.
I have been doing research and can't decide between the Nikon 50mm f/1.8D AF
OR Nikon 50mm f/1.8G AF-S
Can someone please help me?!

I'd recommend the AF-S version as I've had both the D and G version and prefer the performance (IQ) of the newer one.

but a warning, when shooting at large apertures with moving subject, make sure you don't miss focus as anything that isn't in the razor thin DOF will be out of focus.

You might also consider the 50mm f/1.4G or Sigma's 18-35 f/1.8. Having a zoom like this would be far more versatile and not so tight as the 50mm will be on the APS-C cameras such as your D5100.

Though both are excellent, sharp lenses, only the 50mm f/1.8G AF-S has the internal autofocus motor that your D5100 requires.

Your fine D5100 needs Nikkor AF-S lenses so you can auto-focus using the lens.

F/1.8 is the same regardless…

I bet the D is cheaper causing your dilemma. That's because AF (only) does not have an AF motor (kind of odd with that naming scheme but they have their ancient reasons to it if you have been shooting long enough). You will be forced to focus manually. Manual focus with action? Possible… But can you? No choice then, right? Go AF-S!