In similar circumstances, I shoot at 1/60, on shutter priority, at !SO800, with a telephoto lens, rated at 2.8 to 4.5 minimum aperture ( I don't have a choice about the lens, It's a point and shoot!). The ideal would be to shoot with aperture priority, but I use my zoom, which changes the aperture as I zoom in and out. If you have a telephoto lens with the same minimum aperture zoomed in AND out ( and that would be a really nice lens!), you should be able to do this! You need to be fairly close to eliminate the camera wobble associated with zooming your lens all the way out. If you have a vibration reduction lens or sensor, turn that on, as it will be a huge help! And lastly, you will have to use the viewfinder, so you can screw the camera into your eye socket, which will keep the camera steady! One other tip, if you feel the need, you can increase the shutter speed which will underexpose the image a little, and bring the image back out in Photoshop later.
Here are couple examples. I've found that,unless you feel comfortable shooting these pictures in AUTO ( it's do-able, I will explain later in another post), 1/60 at ISO800 is best for inside and stage lighting, if you want to have reasonably focused images, without the graininess, of people in motion.
I hope these are helpful!