Hi there, it all depends on how bad the condition of the bike is. For chrome and paint work I only use Turtle wax, for alloy I use Solvol Autosol, nothing aggressive.
Give the bike a really thorough clean, use a cleaner such as Gunk or paraffin to remove oil and grease, then you can really see what you have.
However if your chrome is really bad then you will have to get a bit rougher with it, for rusty pipes I always used to rub them down with wire wool (Brillo) and used heat proof aluminium paint to make it look better.
For alloy if it is really bad you will have to cut it back to a smooth surface, again Brillo pads (used wet) are good for this or use progressively smoother grades of wet and dry followed up with a metal polish, again my favourite is Solvol Autosol, but there are others.
If the chrome is that bad think about either re chroming, replacing, or if money is tight painting.
Cheers
Den