Remington 572 Rust Problem

I purchased this rifle from a friend. I need to do some work on getting the rust stopped. I attached a photo of some of the rust spots on the barrel. The gun has other areas that have surface rust and others that are a little deep as shown in the photo. What is the best product for removing the rust and keep it from coming back? Thanks D.

Nice, This rifle has many good days left in her, and I can pass it down to my grandson when he gets older.