I don’t have much experience with car detailing either but here’s my suggestions. For polishing, I’d stick with hand polishing since there are so many nooks and crannies in those rims. Or you could try the Mother’s Polishing ball. For compound, I’ve had good results with Meguiars Ultimate Compound On car paint. It’s advertised as a hand or machine polish. For iron removers I like Sonax wheel cleaner. Good luck and let us know how it turns out.
That looks to be a painted/metallic finish. Beware of using a true metal polish, which is for raw aluminum/stainless - it could mar or damage your painted/clearcoated finish. It looks like brake dust and dirt accumulation. Use a wheel cleaner and gentle brush to agitate very well before you step up to mahcine polishing or using a metal polish.