Digital Camera for Christmas

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I thought I'd ask for a digital camera for Christmas, but I don't know what would be good for me. I would use it when I'm having fun with my friends, car shows, and other misc stuff. I took a photography class in high school, but I don't have the knowledge for shutter speeds and apertures down. It would be neat to take small videos with the camera, but I’m not sure what that adds to the price. I was told digital zoom is worthless.

I noticed on other digital cameras, it takes a second for the picture to be taken. Is that common, or is it easy to avoid?

I'd it to have an lcd screen so I can tell what the picture looks like right after I take it.

What are some good options for me?