A Dremel with a wire wheel attachement will quickly and easily remove spot rust like that. Then go over the effected spots with steel wool, clean and degrease, touch up with cold blue, polish with fine steel wool again, then rub in a generous coat of silicone. Quick and easy, it will look much better, though obviously not perfect.
If you really want to go the extra mile because it is a family heirloom, look up THR member Tincan Bandits posts and blog. He does amazing restoration work and gives excellent tips and techniques, most of which you can do at home if you invest the time and elbow grease.
Then, of course, there are professional restoration services, but you get what you pay for and pay you will.
Good luck!