I found a HP 812 refurb at compgeeks.com which was 4 megapixels, ran on AA batteries and does a 3X zoom. I like the size and weight of the camera and pictures at its 3 star (out of 4) setting are good for what I need them for. The camera was 227USD.
At 4 megapixel, the optics will begin to show an issue and in this one you see the trade-off from more lens to more pixels. But I am happy with the balance.
Look at http://www.dpreview.com for more reviews of what you are looking at.
Which camera under $250 would anyone recommend buying for a beginner??? Need advice badly.