Kodak (while I love their professional films and swear by them) cameras are absolutely horrible.
I would go with a canon point and shoot. A family member has the g7 and it is pretty darn good for a point and shoot camera. I have also used a top of the line kodak point and shoot, and it was horrible.
I dont know much about P&S cameras since I shoot with a $7000 digital SLR, but you can never go wrong with Canon.
As for the 10x zoom, they say 10x, just to keep the general consumer less confused. I bet if they put the focal lengths on there everybody would be totally confused. Like said above, an example of 10x is 38-380mm.
You will want to watch out for 'digital zoom' as all it does is crop the image in software, thus greatly losing image quality. Make sure you get one with full optical zoom.