I highly reccommend an Olympus Stylus Tough. I have the highest end ($300-400), 2 of my relatives each have the next model down ($200) and child has the next model down ($120-150 ish) (I would not go lower than the 3rd model down). This camera is water proof to like 10 feet and drop proof from about 6 feet. Mine has been in rivers, oceans, gulfs, water parks, swimming pools for the last 3 years or maybe 4. I have taken thousands of pictures. It has rechargable litium battery.
I hadn't ever had a digital that could fit in my pocket because quality of the picture was more important to me than the camera size. I know lots of people with lots of different cameras and just was not impressed with the photo's. Not that they were all terrible, they just weren't great. So, I had no plans to buy a little camera. Then a friend got this one (1030SW) and wow, oh wow! Now I have one too! I don't think you can go wrong with these! Just remember, don't go with the lowest models, they are made of plastic and are not as good. I would go as high on the models as you can afford - and also do a lot of searching for deals and best prices. I think I got one at BuyDig dot com, but all of them I searched and waited on sales!