If blur is a problem, I'd advise getting a camera that has Image Stabilization. There's a lot that have that now, in everything from compact (relatively) inexpensive models up to (expensive) digital SLRs. You might look at the Canon SD models - that's a very small easy-to-use point-and-shoot, and some of the newer models have image stabilization. I have an older model (SD300) and I LOVE it - it fits in my hand (and I have a small hand!) and 90% of the time it takes great pictures - doesn't do well in low light, though.
If you want something a little larger (though still in the "compact" range) with a larger (6x) zoom, look at the Canon A series - the new A650IS and A720IS both have image stabilization. They can be used as point-and-shoots, but they also have a nice selection of manual features if you are so inclined.
Check out
www.dpreview.com - you can go to the "Buying Guide->Features Search" and plug in the features/price you want and it'll return a list of cameras with those features - usually you end up with a LOT more results than you really want. They have extensive reviews on a fair number of cameras, too.