Unless your cleaning some super high dollar bench rest rifle m
My advice is to keep it simple... I use bore snakes as a rule... some folks don't like em... BUT that's why God made Blonds and Red Heads...Fords and Chevy's..
So..bore snakes per Cal. and a good bore cleaner.. a couple of old tooth brush's and some pipe cleaners ...OH and the smallest paint brush's you can find..not artist brush's.. a good lube.. I like Rem oil..WD 40... hell most anything.. some will scream about wd 40... think "Blond..Red Head"... the latest hot shot product is only equal to the amount of money paid to advertise it and who they pay to say "I USE IT!! " WD 40's been around for ever I've used it for 50 of my years.. never an issue with any part of it... ok Commercial over ... I love Break Free for hard use.. like during a match with a high round count.. I cut up old tee shirts for wipe rags...old towels for something to lay the gun on because I usually clean on the dinner table.. I'm single so I can do as I want... other may need to use caution here...
Just so you know...warm water and soap are two if the best gun cleaning things you can use.. I've taken the grips off my 1911's and stripped them to the basics and tossed them into hot water and dish soap.. let em soak a bit...scrub well with a tooth brush.. rinse with the hottest water you have.. I set them in the oven at 200 for a few minutes and then lube.. never had an issue with this method ... spending a lot of $$ on some high dollar kit is a waste.. I also survived 4 years in the Marines with even less of a kit then this,,
Avoid steel cleaning rods, and remember the muzzle is the part of the barrel most critical to acuracy, so clean from the breach whenever possible. When this is not possible, try to avoid the rod contacting the muzzle.
I'm old school, and prefer Hoppe's #9 bore cleaner, especially since I shoot a lot of surplus ammo thru my ex-military rifles (it's often corrosive, and Hoppes is formulated for this).
Use oil formulated for firearms, 3-In-1 won't cut it.
Avoid plastic bore brushes, they are junk. Use bronze ones.
If you are shooting M1's, either Garand or Carbine; or M1A's, remember that they were made to be properly lubed with grease, not oil. I also use grease on the rails of my 1911 pistols.
And yes, I am one of those who think that WD40 should not be used on a firearm unless it's an emergency.
If you shoot a lot of jacketed bullets thru your rifle, investigate occasionally using a bore cleaner formulated to remove copper fouling. I have a bottle of cleaner made by Remington, there are others that work good also.
You do not need to get all carried away on a high end kit to begin with, just a basic one made by Hoppes or Outers and sold at places like Walmart or most any gun store will get you started.
Oh, and as mentioned already, an old tooth brush is an essential part of your kit.