That Gazelle looks awesome. But there is quite a but if rust around the rear hub. Looks like you have your work cut out.
I have an 88 Gazelle which uses the Sachs Torpedo 3 speed. The coaster brake was hardly working anymore because of all the hardened grease. I think this hub was never serviced. Opened it cleaned it and re-lubricated it again. Now it works like new.
I have had bikes with Sachs 3 speed hubs since the 70s. I grew in Germany and they were everywhere back then. My favorite is the Sachs/SRAM Spectro 3x7. I have got this hub on 3 bikes. Basically bullet proof. However I had a clutch failure and a flange failure on on one of mine about two years ago. Since the local bike stores rejected to work on the internal gear hubs I decided to learn it myself. These are really no rocket science. So whenever one pops up cheap on ebay I grab it since parts are getting rare.