Younq fella, here are some ideas that you might consider for maintaining your rifles. Keep at it, you are showing great interest, wish that there were a lot more your age into this sport. Would enjoy helping you anytime.
Use a bore-guide and put a rag under the front of the bore-guide to catch any solvent squeezed out in the initial pushing of the rod.
Then put solvent on a patch and stab the patch. If you hit the patch in the center it will fit tightest. Moving over a bit from center will make for easier entrance and passage.
When the patch gets out of the muzzle take it off and pull the rod straight back and out.
Repeat with another patch until the carbon reisidue or copper discoloration is no longer evident by the colors on the patches. Don't scrimp on the number of patches, you usually have to use a bunch with most factory barrels. That is why most guys make their own out of flannel, stuff they used to make diapers out of.
Maintaining rifle is NOT cheap and should not be done cheaply, as in cutting corners. Patches, solvent, brushes, grease all cost money but you MUST use the stuff religiously to ensure your rifle is working at its best.
Always use a bronze brush that has the front end looped, not cut-off. Always put four or five drops of carbon solvent on the brush and push it fully through the barrel. You can put a few more drops on it when it passes out the muzzle the first time, then pull it back through and the solvent should be evenly distributed.
Always dry your bore after use, if you are not shooting the rifle for a while leave a film of oil or rust prevent in it. Always dry your chamber with a swab (wool mop) or dry patch and clean out the lug recess with the appropriate tool and swab.
Alwyas brush any brass filings from the bolt face, extractor etc. and clean gunk from the bolt face with a toothbrush or M-16 brush. Drop a couple of drops of carbon solvent on the bolt face and brush it, then wipe with a rag.
Always lube the rear faces of your lugs and the contact location at the base of your bolt handle.
Always wipe your rifle, mounts and scope to remove accumulated dust and dirt, then wipe with a lightly oiled cloth to protect from rust.
End the job by wiping the crown, always a bunch of black stuff there.
At least once a year clean inside the bolt body, wipe the firing pin and coil spring, put a dab of lube on the spring to prevent rust. Remingtons need a tool to take the firing pin assembly out, no sweat it is cheap and quite simple to do. You might be surprised how much crap can accumulate inside a Rem. M-700 bolt.
Good luck.