Here's what I use on my blued guns, after doing a lot of research.
I use:
Breakfree CLP (it's an inexpensive, effective cleaner/lubricant/protectant*)
Flannel patches cut to size (bought in yards at a fabric store.)
An old toothbrush (for places like the ratchet, top strap, etc.)
Q-tips (for places like cylinder notches, barrel extension, etc.)
Toothpicks (for places like cylinder notches, recessed cylinders, etc.)
0000 steel wool heavily laden with CLP and rubbed gently (only ever used for rust-which means only new-to-me guns

)
A bronze bristled toothbrush (for lead buildup on cylinder and barrel extension and used very sparingly.)
Brass cleaning rod.
Nylon "multi-cal" bore brush (Christmas tree shape) for bore and chambers.
Never needed anything more aggressive than CLP with these methods.
*Breakfree CLP because it meets a standard for gun oil. Most gun oils are whatever the manufacturer decides; there are no industry standards or laws regulating the use of the term "gun oil." A firm could literally market repackaged olive oil as gun oil if they wanted to. Breakfree CLP at least meets a military standard of what a gun oil should be. It also does very well in corrosion torture tests, and lubricates grueling environments like an AR15 very well. Just remember in the back of your mind that more guns are ruined by improper cleaning than are worn out from shooting.