On the wheel nuts a quick rub with sandpaper to get the surface rust off, then dunk in a cup of ospho or similar (phosphoric acid) overnight. Then wash/rub down again, another dunk if you need, and hit with some wheel paint (I think some thin plastic over the nut when you use wheel wrench should help save the paint but it wont last forever).
On the wheels, I also agree wheel refinishers are a bit scary as they may suddenly sand blast or get the sander out.... I'd strip remaining paint with a citrus cleaner, really lightly sand any oxidation. Then really wash the wheels with hot water to get the surface clean. Dry really well (in direct sun or near the heater at home). Use an aluminum prep (eastwood has a spray bottle) following their instructions - they may etch the surface for you so you don't need a primer. Then when ready use a rattle can silver wheel spray to finish. I think I had really good experience with the VHT product.
The finish is surprisingly good and will last years in most cases. Those wheels don't have many nooks and cranny's to deal with and that will save heaps of time compared to say a Turbina. I spent less time on the back of the wheels - just clean, get all the flaking paint off (scotch brite pad?), scuff the whole surface (scotch brite pad) and paint (not removing all the old paint if it was solid), if there are big patches with no paint use the aluminum prep again. Ditto the rim facing the tire - nicely painted so that the tire has a good seal.
I've finish magnesium/aluminum blend Ferrari wheels this way minus the aluminum prep but using an aero magnesium prep, and being really light so as not to disturb the Dow7 coating on the magnesium. Recently also refinished a Turbina spare for the alfetta.This all takes some time but really no equipment and the return of effort is worth it (just driving to and from a wheel refinisher takes a few hours in most cases.