Recommendations for HD video camera...

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I'm having a baby in about 10 weeks, and I thought it'd be great if I just record everything he does instead of write it down. Also be more fun later when I can embarass him in front of his friends and future girlfriend(s). So I thought about it, and I figured that with all the technology these days, it'd be pretty sweet if I could capture all the embarassing moments in high def. Does anybody have experience with and/or recommend a high definition video camera for use around the house? I wouldn't even categorize myself as a prosumer, so cheaper is better. Any under 1g?