Noise is better than blur (and much less of a problem than you might think from reading the internet), so don't hesitate to vigorously boost ISO.

Underexposing won't help; it's basically the same as increasing ISO w.r.t. noise. The only time to do this is when you've already maxed out the ISO adjustment.

Consider a "fast fifty" - you can get a 50mm f/1.4 or f/1.8 lens for super cheap.