How to clean her up

My bike is an '81. It was sparkly clean at one time, but now she's all grimy and oxidized. Are there any sure-fire ways to get the oxidation off the engine and bring all the chrome and metal back to its original shine? I tried a dremel tool and mild wire wheel in some small spots, but it leaves lines and takes f-o-r-e-v-e-r cuz the wheel is about 1/4-inch across.

I'm thinking about some fine steel wool and simple green. Anyone tried this? Anyone know what works best? I'm so proud of my first bike, and I wanna make her shine so I can show her off 8)