You can remove surface rust using a 'Brillo' or 'SOS' steel wool pad. I've used this trick for years to remove rust that exists in the creases of my chrome wheels. Just scrub, rinse off and voila! The rust will be gone. Depending on how bad the rusting is, some of the scrubbed areas will reveal the bare metal beneath. The soap in the SOS pads cause these areas to go dark grey or black, which is less visible than brown rust, improving the appearance of the wheel.
My wheels are original, and in pretty good shape considering they're 59 years old. The chroming done on the factory wheels was very good quality, which is why so many of the early wheels look good today.
The centers can be repainted. It's a fiddly job to mask the chrome portions of the webs. I heard you can buy masking templates for this, but don't know where. The wheel centers on my '65 didn't need to be completely repainted. Used POR-15 in a grey color which was a very close match to the original charcoal tone used on these wheels. I used a foam brush and carefully applied the paint inside the wheel webs, keeping a rag handy to quickly wipe off any stray paint that got onto the chromed portions of the wheel. Worked very well, and saved me from masking the wheels first.