Spring cleaning my bike

Spring cleaning projects are in abundance. One of my projects will be to attempt to strip some of the rust from my bike. I have a good looking bike that is in otherwise great condition. It is Schwinn cruiser, only a couple years old and I would like to restore its shine. I know that if the rust has penetrated deeply there is not much hope. I have faith that this has not happened. The best case scenario is if the only remedy is some CLR or another type of cleaning agent.