I bought a Canon Powershot A620 (the 7mp one) which was on special offer at a stupid-low price. The picture quality is good and the optical viewfinder and flip-twist LCD screen make it really versatile. I haven't tried CHDK (open-source replacement firmware) but I have it downloaded somewhere.
Its a real shame Canon stopped making this line of mid-level cameras. They are not so light or small and the 4xAA are a bit heavy but I can live with this.
A small tripod is essential for self portraits and low light shots.
Take a couple of SD cards. You can get them so big they will take all your pics but if one breaks, it takes all your pics with it.
The other really useful feature to consider is a tough/waterproof one such as Olympus Tough 6000.