I have been unable to find any reason why the type of soap makes any difference. If someone can point me to a source I would be grateful. I use laundry low e detergent because it's extra handy. Soap and hot water remove oil, wax and soil. The cirtic acid also helps with any wax.
Any source of citric acid is required to brighten and remove the tarnish from the brass. Any acid will work, but a very weak acid solution using citric acid is a better choice than salt and vinegar. Vinegar with salt creates a small amount of very strong acid in the presence of free oxygen and can rapidly turn shiny golden brass into dull pink pink brass. Too much acid and you get that pinkish coloured brass. Strong acids, although they do the job well, do it too much too fast due to the fact that you end up tumbling for a longer period to use the SS pins for an abrasive. Use a small amount of a mild acid source! Even one big squirt of pure lemon juice works.
If you can find it, powdered Kool aid (no sugar, just the powder) works very well. I found a couple of bargain boxes of Pres. Choice tangerine grapefruit which contain citric acid, colour and artificial flavour. 10g packets and smells kinds fruity. Lemishine is very good but you can't make a tasty drink from it. At 5g or so a use, you'll lose it before you run out.
Use water as hot as you can get it out of the tap. Your hot water might be up to 120-140 degrees depending on the hot water tank setting which should be fine.