FWIW: I have been shooting benchrest style for about 20 years. In that style, the barrel cannot be too clean. I recently started to shoot steel, prone off a bipod, at 500 meters. That is a different game where cold-bore shots matter.
If I get the gun on target at 500 meters then take it home and clean it with my method, the cold bore 500 meter shot will be about 1 foot high and 1 foot to the right. If I leave the gun dirty, my cold bore shot is pretty close but the second shot is on the money. The clean gun takes 2 or 3 shots to get back on the money.
Guidelines
Use a cleaning rod guide. I bought mine from Sinclair; there may be better ones. Use a one-piece coated cleaning rod, I use Bore-Tech and Dewey. If you don't use a rod guide and/or if you use a segmented cleaning rod (steel or aluminum) then it really doesn't matter how you clean the barrel because you are going to booger up the throat or the crown and the gun will stop shooting before the bore gets dirty. If you use a guide and a 1-piece rod, the rest of your system is up to you. The only really wrong things are too much cleaning (every stroke of the cleaning rod is a risk), too much ammonia (for high pressure, high velocity rounds, it aggravates barrel alligator), dirty patches (dirt scratches the barrel), and steel brushes (same as dirty patches, bronze or nylon are best).
My Cleaning Drill
Here is my cleaning drill, your mileage may vary. There is more voodoo about gun cleaning than weirdos at a Trekkie convention.
I use a nylon brush and Ed's Red for 10 careful strokes -- always be careful of the crown. Two dry patches. The goal is to thoroughly moisten the powder fouling with ER and wipe out as much as possible.
1 patch of wipe-out accelerator and 1 patch of wipe-out. Wait 5 or 10 minutes; 1 dry patch. Repeat for a total of 3 cycles. Wipe-out contains some ammonia -- a lot less than Sweet's. Ammonia and copper makes a blue organic compound. That color is the only good thing about ammonia, it tells us if the barrel still has copper in it.
If the 3rd dry patch comes out with blue on it -- blue means that there is still copper in the barrel -- run a patch of JB, 3 patches of Ed's Red and two dry patches. The idea here is: if the barrel is still not clean after 3 cycles of wipe-out then continuing this process means that you run the risk of damaging the barrel with the rod. Accelerate the cleaning process and reduce the rod damage risk by going straight to the nuclear solution. Why not go straight here and skip the wipe-out? Because JB is abrasive and won't help your beautiful 5R rifling.
If the 3rd dry patch doesn't show blue, the barrel is done. If it is close, I may do a 4th cycle. Or maybe not. Sometimes I just slap in some KG12 (just for the hell of it) and two dry patches. KG12 and JB both make the patch slide through the barrel like it was oiled.
When it is done, run a patch of oil, wipe the fluids off the brake and barrel, and put it in the rack. Why oil? Even stainless steel "rusts". And we just finished running metal projectiles through the barrel more than 2,500 feet per second under high temperature and about 55,000 pounds per square inch pressure. Then we clean the snot out of it with abrasive and corrosive stuff. The oil will reduce the chance that oxygen will combine with something in the barrel steel or something that we didn't get out of there and create a problem. If I am taking the gun to the field, I run a dry patch through it to remove most of the oil - if I leave oil in the bore, dirt will collect there.
Make no mistake, a clean barrel is not really clean. Find a guy with a borescope. It will make you wonder why you bother; but a clean gun shoots better than a really dirty one -- benchrest guys don't clean after every match just so they can screw up their barrels. </sarc> Barrels cost $400 a pop even if you buy them in bulk and chamber them yourself.
I put 70 rounds through one of the 7.62 guns last weekend and I didn't clean it at all, just set it in the rack. I will probably put a total of 200 rounds through it then clean it again. An acquaintance with a professional background pointed out that it is hard to clean a gun in a hide, targets won't wait, and clean-barrel cold-bore shots are not consistent.
A properly broken-in barrel with about 50 rounds through it should produce a clean 4th patch every time. In that particular 7.62 gun with about 30 rounds, I will get a clean 3rd patch. That gun has a Kreiger barrel 5R on it. I have a 300 Win Mag with a Bartlein 5R that behaves the same. I have had many other barrels, cleaning depends on the individual barrel. I had a Gary Schneider in 300 win mag that never broke in; other people love them and wouldn't have a different barrel. I think that expensive barrels break in faster, shoot better, longer, and clean up easier. I will buy another Kreiger or Bartlein when I need a new barrel. I have owned Harts and Shilens, that Schneider, and Remington barrels - that was the worst. Threatening to load the weapon, even gesturing in its direction with a round, made the barrel dirty - no shooting required.
Action
I use an AR-10 chamber brush, it looks like the M16/AR15 chamber brush except the chamber bristles are bigger, and a brass pistol rod. That cleans the chamber and the space where the bolt lugs reside - a couple of turns does it. I usually wipe out the bolt rails with Ed's Red then dry them. I put very light oil on the bolt locking surface and the cocking surface. I disassemble the bolt (remove the firing pin and shroud) every time and knock out any crud. For my nicer bolt with the M16 extractor, I occasionally remove the extractor and ejector and clean in there. I put very little oil on anything where dust or dirt could adhere.
I have a fire-forming barrel for the 300 win mag. If I pull the barrel in order to fire form, I pull the action out and really clean in the space where the action sets. Otherwise, I don't fool with the action screws or the action.
Trigger
I have Jewell triggers. I have several. I already bitched to Arnold about how much they cost, "You bastard! I have a $1,200 of your triggers!" He laughed at me. YMMV. I never clean them. I check the pull weight once a year just to be sure. Mine are set to 4 pounds. I have never had one change by itself.
I saw a Jewell trigger stop working once. It was at the Crawfish benchrest match in 1994 or 1995. The shooter went to the line, the gun would not cock, he came back in a panic, borrowed a gun and ammo, went back and shot his match. While he was shooting Arnold heard about the problem, walked over, took out the trigger and disassembled it. When the shooter came back, Arnold was HOT!. The shooter had stoned some surface and Arnold noticed. I suggest that if you ever stone one of Arnold's triggers, don't let him find out.
The official cleaning method is: run naptha (lighter fluid) through it.