It sounds like you want a compact? I love my wee Canon Ixus 800, I got a storming deal on it but it'd still have been a decent buy at full price. 6mp, 4 x optical zoom, which is pretty uncommon in the really small compacts, not bad optics... Not much lag either, though there's enough to be annoying. It's better than I am, put it that way. And it's the size of a fag packet
You can get decent results out of even very budget compacts now, if you don't mind them being old-tech- bulky or slow. I chopped in my old Kodak because it had gone a bit senile, but other than its size (a bit smaller than a typical 35mm compact) it wasn't massively less good than the Canon, and they only set you back about £50 now.