First time runner

No need to fear being stared at if you are new to a treadmill. In my experience most people go about their business. They have other things going on in their mind, like listening to music, watching TV, or being in deep thought rather than targeting the rookie on the treadmill. You can always start at a very slow speed and then gradually speed it up if you are unsure of how balanced you would be by running on a moving carpet. It will feel a bit odd at first, but after that you will get used to it in no time.