I second the Canon. My whole family (extended, too) have some sort of variation of the Canon elph powershot. I have the powershot SD 100 (which is relatively outdated) and I love it. Its small enough to put in your pocket to go out and good enough to take good quality (good enough quality, for me at least.)
My brothers and I just pitched in to buy my mom a new powershot (I forget which one) but it was 200 bucks at PC Richards, 4.0 megapixel and 4x optical zoom. If you're new to the digital photography world, I'd say thats a perfect choice for you.
Oh, and they're very easy to use.