They sell steel brushes, why is a mystery to me, NEVER use a steel brush, copper if you think you need it, and only when you think you need it (if you shoot moly coated bullets, or all lead bullets, you should brush it almost every time you use it, copper fouling is typically MUCH slower-if it appreciably occurs at all for you, you can get away without brushing it out for a long time (years probably if it's just a deer rifle).

Now that that's out of the way here's what I do for bolt actions+ some advice:
****EVERYTHING IS DONE FROM THE RECEIVER END****
-you don't want to damage your crown, and more importantly, it's better to push crap out of your muzzle into the world instead of pushing it backwards into your action-some people claim it also prevents you from interfering with the "grain" of your bbl, i.e. bullets push the "grain" from receiver towards the muzzle, brushing or swabbing muzzle to receiver counteracts this, so you get increased bbl wear and diminished accuracy-I don't know if I believe that, but the fact that I push crap out instead of in is enough arguement for me (except on certain guns that don't allow you to feed from the rear-i.e. semiauto .22's like the Marlin Mod 60 or Ruger Mark II pistols)

-I strongly recommend using a bore guide, they're cheap enough, and they really help, it kind of sucks if you've got 15different bolt guns and have to get one that fits each of them, but they're worth the cost IMHO, if for no other reason than that they keep your rod straighter as it feeds through the action and chamber=more true in the bbl.

-Get a good one piece cleaning rod, those three piece aluminum rods are crap, they come unscrewed with your rifling, they flex a little so the "seams" where they screw together drag on your bore (aluminum SHOULDN'T scratch a steel bbl, but I don't care to risk it, or they plumb bend when you try to push them.

-Not everyone does it, but I make a point of it and firmly believe in it--always take your tip off when you pull the brush back through-whether you're taking your brush off or pulling the patches out of the jags, never pull a dirty patch back through, or a dirty brush-the bristles will flex one way and collect a lot of crap, when you pull them back, they can open up and dump more stuff back in, in either case it'll end you up swabbing longer.

-Silicon patches are pricey, but they're awesome for breaking stuff out. They're usually too coarse (and expensive) that when I get the "bulk" of the crap out, I'll swap to cheaper fabric patches, just so I don't increase my bbl wear.

FOR THE BBL:
1)Run a solvent soaked (pretty juicy) patch through and let it sit for a while-I'll ususally clean 2-3guns at a time so I can start another one while I'm waiting-even if I'm taking one out of the safe just to put fresh oil on it.

2)If need be, I'll then run one more patch through dry or lightly solvented to get the big chunks that loosened up, then brush it maybe 2-3times.

3)Then run a solvented patch through (heavily soaked), let it sit a little while longer,

4)Then start swabbing (I start with lightly solvent soaked silicon patches until the majority of the crap out, then switch to fabric patches/solvent until they come out pretty clean, then I switch to fabric/oil for the last few), at first you might get away with flipping the patch over, use one side then the other, until you get the majority of the gunk out, but once it starts getting cleaner, use them only once...once one comes out clean, run a dry one through once or twice, then run a lightly oiled one (or two)through to coat the bore.

5)If it's going to be sitting for any amount of time, i.e. the whole off season, either grease the bore or heavily oil it, then before you shoot again, run a dry patch through-My granddad used to pack his bbls with bearing grease literally full from chamber to muzzle during the off season.

INTERNALS & EXTERNALS:
-NEVER GET OIL ON WOOD, gun oils shrink and discolor wood, look at old shotguns-especially pumps, you can tell where guys just rubbed oil on the outside of their gun, and got some on their stocks, they're puckered a bit where the stock meets the receiver and they'll have a black/dark line running along the seam-it's even uglier on wood stocked bolt guns.

-Anything that comes into contact with ANYTHING needs cleaned and oiled-don't be lazy, pull everything you can apart (owners manual), clean and lube it-I've seen lots of rifles with beautiful appearances that have the bbl/receiver under the stock almost rotted away-moisture gets in there and no one ever took it apart far enough while cleaning it to oil/treat it. Get ALL of the moving parts lightly oiled (at this point, if you're putting it up for the year you might grease them-that way you can rest a little easier over the off season), clean all of the carbon fouling from the action-it gets into WEIRD places sometimes, check everything out, clean out any dust, hairs, sawdust (from factory), carbon, etc. and oil it.

-Take special care of your bolt/bolt tracks/bolt face/firing pin assy...if your gun has a removeable firing pin (some take 3 men, a monkey, and a DANG good gunsmith to reassemble), take it out, clean the pin assy, pin hole, and pin housing and oil/grease it well (I like a light grease instead of oils in here, they tend to hold up better and lubricate just as well). You don't want something getting in there and wearing your pin prematurely, or heaven forbid lock it up-even just for a second, hangfires can be deadly. You also need to keep your tracks clean, that way you don't accelerate your wear (dust is just really fine sandpaper, work a dirty bolt too long and it loosens up quickly).

-Rub a light coat of oil on the exterior, to prevent it from rusting, a light oil with a "protective finish" in it is best for this (it's really best for all of it, but more important here).

-Take care of your scope, oil it too, but don't get ANY on the lenses, NEVER wipe the lenses with anything but lense cloth, the red shine on lenses is a chemical film that protects the lenses, rubbing it off will let your glass get scratched more easily. Use dust covers, flip open kinds are great, but any cover is better than none. Blow excessive dust out (with an air hose), don't rub it, dust is fine sand paper, so you can scratch your lense just rubbing it out. Luepold scope tool is a great tool, a brush on one end to pick up dust and a dauber on the other to redistribute the film and fine clean it.

I know that was really long, I've actually left out several things that I do, but I'm pickier than most, it also takes a LOT longer to say than do, and I think it's really important that such intimate attention to detail is taken-it extends the life of your gun, preserves consistancy (accuracy), preserves resale value (nothing cheaper than a rusted gun), and assures maximum reliability.

I'm pretty picky when it comes to my guns, they're either dirty (just used), or spotless, I never half-@$$ it when it comes to cleaning my guns. When I'm at the range, they get a good field cleaning before going back in the case, and a thorough cleaning (all of the above) as soon as I get home, then they go back in the safe.