Mild acids that are food grade are great because you don't have to worry about occupational health exposure. A lot of people use vinegar. I use citric acid -- which you can find in the grocery store in the spices section. Citric acid is what makes sour candies sour. You buy it as a powder.

I mix a little water and citric acid and let the part soak in it, then brush with a soft wire brush (not steel wire, as it's too hard and will scratch the parts too much).

But, as a tangent, buying stronger acids is pretty easy, depending on the acid. Hydrochloric acid is sold in hardware stores as muriatic acid. Sulphuric acid is used to recharge lead-acid batteries. You'll have a harder time finding nitric acid (because people can make explosives with it) or hydrofluoric acid (cause it is actually deadly as fuck), but industrial suppliers often have them. I wouldn't handle any of these without some training. Even muriatic acid will off-gas chlorine and cause all the tools in your shop to rust if stored improperly. (From experience.)