Most cameras also let you pre-set the shutter speed and ISO. You can pre-set these to higher numbers (400 should be more than sufficient for any portrait type shots and that should totally eliminate the blurriness. However, it will come at a slight cost in picture quality and the images will be slightly more grainy than usual.

That being said I'm going to have to throw in a pitch for any of the cameras in Canon's Powershot series. If your primary interest is personal photography, I would suggest a camera that's small and light like the SD300/400/500 (in ascending order of mega pixel and price), so you can take it with you all of the time. If you do a lot of vacation photography or like to zoom in, something like the S2 1S would be your best bet. If neither size nor zoom are a concern, and you're looking for a low cost option, the A500 is the way to go. Usually, digital SLRs are out of the price range for most personal photographers, and most people consider them too large to carry around on a regular basis. However, recently there have been a number of (comparatively) low end models released that are really quite nice like the Digital Rebel XT.

I hope that helps.