My mom has an older Kodak Easyshare and I don't like it, the pictures are icky. I've also had friends that had Kodaks and the pictures were crap too.
I have a Sony Cybershot, it's an older one from last year so it's only 7.2 megapixels but it takes killer pictures. I LOVE it. Before that, I had an older one from years ago and it still took awesome pictures but I sold it since we got a newer one. I definitely recommend a Cybershot AND a huge memory card, as you'll take tons of pictures and love them so you'll take even more.