Advice needed: cleaning / restoring parts on a vintage Peugeot
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.