A noisey shot, is better than a shot that is not acceptably sharp
Learn the capability of your camera - same room, same lighting, and bump the ISO up until you reach a limit that you're happy with from an IQ perspective - but don't be afraid of noise.
I would actually recommend using manual mode, as you will have full control over the camera, and it's not that difficult once you understand the effect that aperture, shutter and ISO have. I personally found aperture priority etc confusing when I started out, as settings would change wildly between photos, dependent on the light.
For example, with a simple portrait you may decide you want a relatively shallow depth of field at f2.2, but still keeping face in focus. You can then adjust your shutter to an acceptable handheld speed for a non moving subject (say 1/200) and then raise the ISO until the image is exposed properly.
If the exposure is still too dark you would essentially drop the shutter speed or open your aperture - or add more light!
If you're over exposed, you could narrow your aperture, increase your shutter or lower your ISO.
I've over simplied things really into a couple of paragraphs, but hopefully you can see it's not too complicated to put into practice, once the basic concepts are grasped.
Good luck with it