I resisted the temptation, but...
There are many products available to use for different tasks. Your cleaning regimen can be as complicated or as simple as you like it to be.
Myself I have many different solvents and lubricants, most of the bottles nearly full. I guess I am a sucker for the "newest and best" product. If I am shooting jacketed bullets, I will use T.M. solvent, as it doesn't smell too awful bad, and does a good job removing both carbon/powder residue and jacket fouling from the barrel. That or the foaming Wipe Out stuff.
If I am shooting cast bullets I'll use either Ballistol or Breakfree or sometimes Hoppes #9.
Sometimes I'll use a loop to hold the patch, other times a jag, yet others the Parker Hale style jag. For my 6.5x47Lapua I use one of those felt plug deals instead of patches.
On badly copper fouled barrels, the little felt plugs and JB Bore Paste can be helpful.
I have an old automotive chamois I have cut 5" pieces of over the years which is nearly saturated with Break Free. I use it to wipe down the outsides of firearms before storage to prevent rusting.
I can see that I have spent far too much time and money in attempting to tackle what could be a quick and easy task. Since I find cleanup after cast bullets to be a whole lot simpler, I find myself shooting firearms that are either optimized for cast bullets, or which tend to shoot them well. Jacket fouling is some stubborn stuff, and either requires mechanical (read elbow grease) means or stronger chemical means to remove. That and bores shot with cast bullets seem to last longer.