Ten-Finger Exercises

Camera shopping, need help!

I've been looking for a new camera. Well, to tell the truth, I've been looking for my old camera as well. It just happens that my camera and Bill's office camera were identical, nearly. He could tell the difference. I couldn't. The problem was, they became interchangeable, and now one is missing. So it has to be mine. (Is there an icon for 'pout?')

The article I read said that one only needs 3 pixels for downloading onto the net, and in fact, more pixels may make it harder. What I had was 6 pixels, and I did have trouble. It also had a 12X optical zoom, and I don't think I'd want to do without that. But maybe, since I don't intend to print big pictures, one with fewer pixels would be better.

If it sounds as if I don't really know what I'm talking about, okay, the jig is up. I don't. i'm a person who still doesn't really know how electricity gets out of the wall and into the cord to the vacuum cleaner, let alone to the light bulb. Well, that's exaggerating somewhat. In theory, I sort of know, well enough to explain it to a six-year-old. That's about my level.
But as far as actually understanding it goes, well, let's just say I'm a whiz at math compared to my knowledge of physics.

So, if you know much about it, how important would you say these features are:
rechargeable batteries, manual control of aperture and shutter speed, and image stabilization?

Any recommendations?