For removing rust, you can use CLR. It, and most other rust removal products are Phosphoric Acid. The reaction changes the iron oxide, which is why you can paint over it.
Here is my suggestion:
Chrome Fork Stantions and lower triple tree - CLR or similar rust removal, followed by a good metal polish (I like Autosol as well) followed by a good coat of automotive wax. For areas you can wax easily, use some Pledge, or similar furniture polish.
Frame & Painted surfaces - CLR, then some zinc chromate primer, then your top coat, and after curing, some wax.
Wheels - mostly yours look like they need a good clean with soap and water, with a stiff brush. If you have stains that won't come off, try the metal cleaner, or if they really won't come clean, you can use some automotive aluminium wheel cleaner, followed by the Autosol, followed by some wax.
Generally, washing and waxing regularly will keep the "iron oxide" monster under control.