Once you have cleaned your wheels properly get them Ceramic coated as it makes future cleaning MUCH easier!
Rims and most metal parts clean nicely (and effortlessly) with a plain cloth and WD40, which is bound to be hanging around on your shelf. For the rims in particular, I would also advise a run with a dry cloth straight after, just to pick any WD40 residue/excess (in order to avoid dust particles from sticking on it after the first ride).
Wd40 is nice to remove the dirt but will let your wheels greasy (can't find better word... Sorry with my English ) Then I use Autoglym clean wheels. It does it perfect. As a french, I should ban English products but.....
But Italian products are fine… Ooh la la… Quelle horreur, peut-être un cyclemotor Peugeot pour le Monsieur? Greasy would be a good description. Seems your use of English is better than that of most English people.
