Firstly, don't let the dirt win. Keeping your wheels (or anything) clean is easier than putting it off, eventually facing a bona fide mess. Next, if you can raise the wheels up to your level, or at least spinning freely, life will be better. I'm fortunate to have a lift, and if I jack the wheel so it's free to rotate, then use minimal water with an old towel to catch the drippings, things go much more smoothly.
If chain goop is present, I use WD-40 on a paper towel to wipe it clean, followed by a water-based degreaser then a rinse. But getting in the corners and crevices requires a tool. A firm toothbrush or small detailing scrub brush works okay, but my favorite is the Sonic Scrubbers oscillating cleaning brush system.
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This paint touchup is a quick and simple "5-foot" cosmetic cleanup and will likely need to be repeated every year or two.
Lastly, using a quality wax type chain lube and wiping the excess after application (use a throw-away rag wetted with WD-40) will help keep chain lube where it belongs — on the chain and off your wheels.
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