I use Barkeeper's Friend to remove rust on the chrome. The active ingredient is oxalic acid. You can buy pure oxalic acid for derusting heavily oxided metal, but this bike won't need that. Make a paste with the powder and water in a small can like a tuna can. Apply with a damp rag, let set, rub off, then rinse with clean water.
Mild soap and water to remove the dirt. Any dishwashing liquid or carwash soap will do.
A degreaser for the grease and oil on the hub, and likely the handgrips. A good cleaner called Awesome is available at the dollar store. If it is especially thick, then I use a typical automotive engine degreaser.
A good car wax with mild abrasives to shine up the paintwork.