DSLRs-enable me

[rach3975]

I'm using a point and shoot now and becoming increasingly unhappy with it. I'm trying to decide whether to start saving for a DSLR and if so, about how much I'll need to save up. Can you point me to some good basic cameras and lenses for my situation?

Stuff you might need to know:
*I mostly shoot my kids, and they rarely pose for me. I'm looking for something that can snap the photo quickly and clearly during the one moment that they look up from their activity or while they're in motion. (That isn't happening with my p&s, though it takes good photos under ideal conditions.)

*I'll be using it in full auto, though eventually I'll probably put in the time to learn to shoot in manual.

*I probably shoot an equal number of indoor and outdoor photos. Our lighting indoors varies from good to moderate. I wouldn't call it low, but in photography terms some of it might be. Outdoors I'm usually near the kids, but not so near that I shoot without a zoom.

Thanks!