Cleaning a gun is not rocket science. I've done it pretty much the same way for over 50yrs. I have made only one change I recall. That is cleaning a bolt action from the breach rather than the muzzle. I have heard all the talk about wear on the muzzle and the throat from the cleaning rod rubbing, I don't believe a word of it. Try this experiment. take a steel rod and rub it in a steel plate and tell me how long it tales to make a measureable difference where the rod touch's. Do the same thing with an aluminum rod. Aluminum is a lot softer than steel and the aluminum may wear but not the steel! I don't care for steel rods because they can rust. I perfer not spending time cleaning and lubing a cleaning rod. Simply wipe one off with a clean rag, sometimes a dirty rag.
Warren Page wrote a great book called "The Accurate Rifle". About cleaning solvent's he had this to say, "I always use Hoppe's; I like the way it smells"! Tell you anything? Hoppe's has been my favorite for a lot of years. I also liked to use Outers now and then but, Hoppe's does smell better. I also have Sweet's and don't use it a lot. Very agressive but does a good job removing metal fouling. Smells terrible. I have never tried much of anything else, why? No need! I could get along with just Hoppe's #9 or Outers and never worry about my guns. I do not and never have used one of those things that keeps the rod centered in the chamber, bore guide. If you need one of those then I suggest you are using to tight a patch. Patch does not need to go thru the barrel like a window squeege.
To much oil and cleaning solvent hitting the wood will in time soften the wood. Simply wipe it off when your finished. The rear tang area get's the most cleaning fluid in it unless you take your gun apart to clean it, I only do that once in a while. But I do pay attention to how much solvent I use and watch for it on the rear tang area. The problem with that area is soft wood there will effect the bedding, makes the rifle shoot different! The other point of bedding is the recoil lug and I'm not sure how you'd get solvent in there without trying.
I never ever take the trigger apart to clean but now and then I do used compressed air to blow it out. Just don't use enough solvent or oil to let it drip down there. And watch the bolt face. You swab it with to much oil, even if you wipe it off good after your done, you wwill get some oil and solvent inside the fireing pin hole. Over a period of time that solvent and/or oil will mix with carbon deposits from fireing and can plug up the bolt enough to keep the fireing pin from hitting the priner hard enough to fire the round.
I don't often take my guns apart but I do clean and lube around the barrel. I use old t-shirt's for rags. Put a little oil on a strip of t-shirt and run it down the barrel like a dollar bill. all my rifles get free floated barrels, the t-shirt will go.
It is not necessary to use so much solvent or oil that you might just as well throw the gun in a bath tube of the stuff, just a bit to clean it. Think about a good fitting patch carrying a lot of solvent down the barrel. It doesn't carry all that solvent. Rather it start's in the chamber, hits the lead and squeeze's out extra solvent into the chamber. That solvent serves no purpose other than giving you a chamber that needs extra cleaning to get the solvent out of it that probably should not have been there in the first place.
I do like to run a damp patch of solvent down the barrel in place of oil. Then leave it sit overnight and run a dry patch thru and you'll get coper fouling with the dry patch in the morning. That's stuff you didn't get out that will probably effect nothing.
With all the cleaning stuff and oil avaliable, it's easy to turn a rifle cleaning into a project but there really is no need. Every body promotes their cleaner's and oils as the best. They need to to justify people buying the stuff. Unless your shooting a match rifle, the bore guide is a product thought to be needed by a huge amount nof people. I'll bet that would not have helped a match rifle one bit in 1950 and those rifles shot better than the vast majority of hunting rifles today! Think about that. Advertising has sold a lot of people on the need for bore guides, plastic coated rods ect. that's all done to turn a profit. You don't really think anyone is going to say their stuff is as good as anyone else's but no better do you? If it's not better, why change.
Don't get lost in the cleaning process. Unless you have a life time of junk in the barrel, spend time re-bedding and you'll normally see more difference in group size's than any cleaning program. learn to shoot right and the result will be more improvement than cleaning. The purpose of cleaning is to remove the powder residue and some of the copper fouling in the barrel. If you clean all the copper out of a barrel, you'll find you have to put some back to get the rifle shooting well again. So you can spend an extra 20 min to hour cleaning all that nasty stuff out of the barrel but the first shot you fire thru the barrel with have copper fouling again and probably won't shoot to the same point of aim. That's where the fouling shots come in. Fouling shots, where do you thing the term came from?
Now ypu can go thru all the rituals and in the end will have worked longer, not got much if any lifetime out of your barrel and spent amore money of cleaning stuff. You'll feel better about it and won't have accomplished much it anythng at all. sometime's feeling good is worth the effort so go for it if you want!