Portraits? Then use a 50mm f/1.8 lens (affordable, fast, sharp) and shoot in Aperture (A/Av) mode with it wide open (preferably by window light).

Look at this recent available-light shot of a student:

This gets you the dual advantages of low-light ability (no flash needed!) and blurry backgrounds. As long as you make sure the closest eye is the sharpest.

So, set your camera to the widest aperture (the smallest F-number), use high enough ISO (indoors this might be 400-800 ISO), and use one focus spot, and aim that spot at the closest eye. Click!