best thing for chrome wheels is very simple.
put a couple drops of Dawn Dish Soap in a pan of hot water, and use a lint free towel or a microfiber towel. spray the wheels off, then dip your towel in the hot water and soap, and gently wipe all of the dirt off...rinsing as necessary.
once they are clean, take a dry lint free or microfiber towel and dry them off.
I use a shop vac to suck all the water out of the lug nut wells, and then I dry mine off with a microfiber towel.
It's also a good idea to use some turtle wax on them as it puts a protective film over the chrome, but it's not visible to the eye, and makes the chrome look pretty good.