You have described three different things. The first thing you want is a camera with little shutter lag. This is the time it takes between when you press the button, to when the picture is actually taken. The second is shot-to-shot speed, the camera's ability to be able to take a photo and be ready to take a second photo. As for the last thing, your photos being blurry could be caused by not using a fast enough shutter speed to freeze the subject, or not holding the camera steady. Some cameras have image stabilization which will "fix" an unsteady hand. As for shutter speed, all cameras have a fast enough speed. You either need to set it manually or use the appropriate mode (most cameras have a sports mode).
I have been searching for the best camera for a long time! I am looking for a compact digital camera that has a fast shutter speed. I believe that is the correct term, basically i don't want to wait 5 minutes after taking the picture for it to appear on the screen. Also, I am looking for a camera that takes sharp pictures. In the past I have had cameras that take quick pictures but then the pictures are slightly blurry or fuzzy.