Advice needed: cleaning / restoring parts on a vintage Peugeot I've got a vintage Peugeot racer bicycle that's needs some restoration. It's in pretty decent condition given its age (1970-1980s), but a everything could probably do with a good clean and degrease and oil to get it looking really good again. 

The frame isn't too dented or pitted which is good, it's the commonly worn parts that need some attention. Parts such as the crank, derailleur, rims, spokes etc that have the odd scuff, bit of rust or bits of metal that are looking pretty mucky and has lost their lovely metallic or mirror finish.  the stain less steel or to get the chrome looking shiny and mirrored again? 

What would people recommend to start cleaning these things with? Any thing that's good for getting rid of all that muck and grime?
For just wiping down the frame, dilute dishwashing detergent in water is fine. 

For tougher caked on grease, I find that any citrus based cleaner that you find in your local bike shop or auto parts store tends to work well. The only caution is that it shouldn't attack rubber tires - but anything in a bike shop or auto parts store usually won't.

The usual cautions about not spraying the cleaning fluid directly into axles or bottom brackets apply. Best to spray it onto a rag first and then wipe. 

If it's too powerful, it might take off some decals so you can also dilute the cleaner.

For polishing chrome and steel, I like Barkeeper's Friend after degreasing. It's not too abrasive and does the shiny.