Hi Alfred, the Sony compacts seem to have some of the best shake-reduction systems that I've come across. With a decent sized screen on the back (rather than a viewfinder) you should be able to see the focus the camera has locke onto.
Compact camera models multiply like rabbits, so it's very easy to lose track of what's current. I have a Sony DSC-HX9V that I use for every day shots (when I don't want to carry a DSLR or film camera) and high definition video. The IS (image stabiliser/antishake) is so good it's like having the camera on a steadicam. However, there are already three replacement for this model announced by Sony..
Budget makes a big difference, but so do ergonomics. Much as I love using the HX9V I do find a couple of the buttons to be fiddly-small.
I strongly recommend you nip into your local Jessops, Jacobs, camera shop (or Warehouse Express if you're near Norwich) and get a hand-on feel of at least six different models from several manufacturers. Leave your wallet at home, and don't buy anything on your first trip. When you can tell us what feels the most comfortable, we can give more advice on the features/specifications and comparisons between similar size/shape models.