Unfortunately, we do not make digital camera or equipment recommendations. Below you will find a resource which can help you in your search.
Saying that, you will be able to find a digital camera which meets your requirements, but you may have to pay a little more than you expect. If you shop around, you most likely can find one for about $450-550. Today's digicams in that price range typically are 4-5 megapixels.
As you know, image stabilization is a technology which helps prevent images from becoming blurry by reducing vibration due to camera shake. It works well but is not perfect.
Another type of image stabilization, developed by Nikon, is BSS (Best Shot Selector). The camera takes up to 10 shots while the shutter-release button is depressed. The camera then compares the series and saves the image with the highest level of detail to the memory card.
Features and price search:http://www.dpreview.com/reviews/compare.asp