Hey Charlie. A have moved up to a new camera myself. The one I have is very expensive, but has it's own rechargeable battery. Battery life is no longer an issue for me thankfully.
When I had my other camera it did OK with batteries. It was a Nikon Coolpix 990. It took 4 AA batteries. I bought a few sets of rechargeable and that worked out well for me.
I know a lot of the newer point and shoot cameras now have theirs own proprietary rechargeable batteries and the battery life seems to be getting better and better each year.
As far as which camera to suggest, that is sort of like which knife you should buy. It is a very personal decision that is different for everyone. My wifes camera is very small so it can fit in her purse. That is not an issue for me so my camera is much much larger.
My suggestion would be to stick with tried and true camera makers (like Nikon, Fugi, Canon, etc.). I would not recommend buying a camera from a company that makes things other than cameras primarily.
Check out epinions.com for some reviews. That site will give you some great info and it will talk about battery life.