Your scenario of the bird opening it's wings involves two different things. The "shutter lag" is the time from when you click the shutter to the time it takes the photo. A fast shutter lag means it would be able to take the photo almost instantly right after you click the shutter.
The second part was that you didn't want it to be blurry. This involves "shutter speed", the amount of time that the shutter stays open to properly expose the scene.
The shutter lag is easy to found out on a camera but the shutter speed is dependent on the lens of the camera and how much light the scene has. I couldn't tell you any camera that will guarantee a non-blurry image in any situation.
I am an amateur when it comes to photography but I would like to pursue it more. I am looking for a camera that is great for still shots, I don't care too much about video recording, and I really want it (and this is at the top my list) to capture all the colors since I mainly take scenic shots. I also want it to have a high resolution and zoom. Since I am an amateur I need it to easily shoot and not be too sensitive to the tiniest bit of movement, If I am taking a pick of a bird for example, and the bird suddenly opens it's wings I want the camera to capture that and not get blurry. I heard about slow shutter, I am not quite sure about it but a friend recommended that I get a camera with that. Now I need a camera that is really durable and doesn't easily break. I live in a small town so it would be pretty difficult to find someone nearby to fix it. Price isn't too much of an issue I'll save up all year if I have to, but it would be nice if the price range wasn't over $850. Does anyone have any recommendations?