With a new rugrat I'm assuming money might be a bit tight so here's another option. One of my cameras is a Panasonic fz28. It shoots good 720p video and good quality pics. It's got a giant zoom range and many settings plus you can fit it with all the lens filters and such you can with an SLR. I think out of the box it's around $400.
Here's a sample I shot of some kids just to give you an idea. You can click through and go HD mode to see the quality. It's not going to rival the DSLRs at 1080, but for sending videos to the grandparents it's pretty good.
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