I'm no expert but I've found that learning as you go along gives you a "feel" for the job.
There are too many different types of metal involved to be able to publish a step by step guaranteed method , but the stages of the process could be compiled.
I'm pretty sure the main points would be not to remove too much metal,
work along the full length of the barrel/s , remember that grease and oil are your enemies until you're finished,
If you're not quite happy with your prep work, you're very probably right,
Never give up - most blotches and blemishes can be worked on again until they're fixed,
Don't leave solutions on too long ! It's easier to do another pass than it is to remove pits ( and more metal ) !
Don't leave solution in the bores !
Be prepared to take extra time to carefully work on the breach and muzzle ends so you don't round off the corners
Have more than one rust solution at hand, sometimes your favourite simply won't work yet another will
Don't try and fix oval or dented muzzle ends by tapping a cone or drift in unless you're a dab hand at it and know you'll get it right, a shotgun is not a blunderbus !

Be prepared to sit with your head in your hands or shed tears when trying to black sleeved guns where two completely different metals make up the two parts or you have leaky grease or flux filled joints that only leak after you have cleaned them 17 times already !
Just keep at it, I was extremely grateful for a few tips from an expert barrel browner on this forum who took time to tell me that if it doesn't work straight away, keep trying, he said that over time you'll see what's happening or not happening and experience will pay dividends.
It's true too. After all the hitches and sore fingers, when a pair of barrels comes out well and you can see your smiling face reflected in the lovely deep finish, it's extremely satisfying.
Oh, and don't forget which safe place you've left the sight bead and try not to be tempted to play with anything that starts with mercur.....