I've been really happy with the Cannon Elph Powershots, I have a couple of them now and they take a great picture, are small enough to put in your pocket, plus you can get a waterproof housing for them making them great for diving or shower pictures. They recycle fast and take the first picture fast... For what it's sounding like you want it for you can't go wrong. Pick up a second hand one cheap off ebay and use it as your beat around camera.
http://www.usa.canon.com/consumer/co...categoryid=113
For some real fun pick up one of these...
http://sanyodigital.com/e1.aspx It's a cheap waterproof digital video camcorder and 6 meg pix camera with flash all in one. The recycle time on the cameras a little slow but it also takes a great picture is small enough to again, put in your pocket and is built solid. I bought one for my wife to put into the baby bag and she uses it with the kids everywhere now. (Think Pool, running in the sprinkler, bath time etc...) Really gives you a worry free chance to shoot just about anywhere and anything. PLLUS you don't have to worry if a bottle opens on accident and soaks everything in the bag.... (has happened ruining a lesser camera)
There are a lot of other waterproof mini handhelds out there. Another suggestion would be to find one that you think you would like and read the user reviews over at amazon... they are honest and usually right on the money.