The criteria I used to decide were as follows.
1. Point and shoot vs SLR
Point and shoot is less expensive, lighter, and more compact. It also is slower to boot up and has a shutter lag (ie press the button and wait for a half a second or so before the picture is taken) that can be frustrating with moving objects. Your lens options are limited.
SLR is more expensive, bigger, and heavier. Most of them can instantly take a picture when you turn them on and have no shutter lag, you press the button and it takes the picture right then. You can also put any number of lenses on if you are inclinded toward that sort of thing. This means that if you want to have better control over depth of field you will be able to do that much better with SLR lenses. Good lenses are a money pit...fair warning...but oh are they fun
2. Decide which brand you want, they all seem to have good and bad points. I read alot on
www.Dpreview.com
3. Go to a store if possible and try holding the camera and try taking some pictures (you might need to bring your own batteries and flash card).
This is just the start of the digital camera equipment list...then you have to get a printer that will make nice pictures...then you will wonder why the pictures may not look like what you have on the screen so you will have to get your monitor and printer profiled...I got sick of paying so much for ink that I plumbed my printer up with hoses and now buy ink in bottles and never have to change the cartridges

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Enjoy.