One of my other hobbies is restoring old tools. Whilst Brian is right and the only bit that really matters from a practical point of view is the sharp bit at the end what you need to do depends upon what you want to achieve.
For a quick clean up, wire wool or abrasive pads will remove light rust. A rust removing gel like
Hammerite Rust Remover Gel will remove anything more serious.
If you get serious about restoring tools then
Shield Technology Corrosion Control Products are very effective but also expensive.
Once your tools are free from rust, one of the best ways to protect them is a wipe over with
camellia oil which will protect the steel but will not stain wood.