Express/cold bluing and browning solutions are chemical applications, wipe on/wipe off and done - not very durable and results may vary.
Rust or "slow-rust" bluing and/or browning is pretty much as everyone says, convince your metal to rust then heat and card off the loose scale.
While definitely cheaper you are going to want to test a roll your own solution first, so there is a bit of time involved there (like several days) hope you are not in a hurry.
Your most useful piece of kit is gonna be a sweatbox - will move things along significantly.
Your goal is to produce very even fine-grained rust - most internet recipes suggested are far too "hot" and result in flaking and pitting rather than a fine dusting. If someone suggests a recipe, cut it in half for testing.
Most browning solutions can be used for bluing and browning (to some degree) as mentioned converting red oxide to black oxide is jut applying heat, generally by boiling or just pouring boiling water over the item - you can control the colour by the temperature of the water. Some guys use steam... never tried that.
You don't actually need metals added to acidic compounds - while they sometimes seem to affect the final colour, mostly what they do is deactivate the acid (effectively diluting the solution ~ a good thing).
I've heard of people using mustard, table salt and urine (not all together) my best results have been with various ferric chloride solutions.
I've used PJs (still have some) a bit of a hybrid as you don't wait for the barrel to rust and MUST boil it for like 10 minutes between turns. Very time consuming but excellent results.
A good rule of thumb, if any solution you make stings your eyes, burns or irritates your skin or eats a hole in your welding table - it's too hot, you should be able to have an accidental spill and not need poison control involved. (not saying you don't need to use safety equipment.. use your brain - it's acid)
Good luck!