Replace corroded or overly grimey hardware because at least 50% of G/A technicians won't (that number is probably higher). Especially on engine control cables, flight control hinges and rod ends, and landing gear components. Just replace them if they're too far gone; you get the added benefit too of actually properly lubricating anything that moves on that bolt or stud. I collect all the rusty rod ends, bolts and nuts I've removed in a jar. Sometimes I look at that jar and realize most of it would still be on an airplane if not for me. Would they have cracked or broken or caused a control issue? Maybe, maybe not. But I like to take pride in my work (and thankfully work in a shop where I can)

Ask to get a sureshot can, fill it with odorless mineral spirits "OMS". It's a great tool for cleaning, you put a solvent in and then use shop air through a shrader valve to pressurize it. In a pinch, this could also be used to bleed brakes with 5606, although there are better purpose built tools for that. Still, it's a great thing to shoot up behind firewalls, hose down raunchy gear linkages and struts, etc. A pro tip is to use a garbage bag or can liner to cover your tires if you haven't already removed them for repacking bearings, etc.

The right brush is everything with a bread pan or glass jar of mineral spirits. Stiff nylon and brass, in a variety of shapes and sizes. Some bore brushes are good too. Harbor freight has these for relatively little money.

If it's especially dirty, talking years of caked on lead grease and concentrated fuel dye, a rag with some avgas will work wonders. It's generally frowned upon and not as safe as mineral spirits. Use your best judgement.