Rods NOT to buy:
Screw-together jointed rods.
The brass and aluminum will allow grit to embed and this will damage the muzzle and bore.
Screw together rods always have a bit of a step where they join and this can really damage the muzzle.
The best rods are either one piece uncoated stainless steel or the new carbon fiber.
The coated rods coating never stays on and scrapes off.
Many Match shooters are now using carbon fiber because they're either perfectly straight, or they're broken.
For all rifle and pistol rods, buy a cone-shaped brass muzzle guide, unless it's a rod that will be used ONLY to clean from the chamber.
For pistol rods buy one piece stainless steel. Unless you have a barrel over 6" you only need two rods. One for .22 and one up to .45, and if you want you can get by with only one for everything. I prefer one for .22 and one for every thing else due to the small diameter of the .22.
For shotguns, you usually only need one rod that will fit everything. You can get by with aluminum on shotguns because the muzzle isn't as critical as with rifled arms, and you can almost always clean from the chamber end.
You can also use jointed shotgun rods for the same reason.
The chamber brush kit is good, since modern shotguns tend to build up not only carbon fouling, but plastic too. Moisture can infiltrate under the fouling and rust the chamber.
Old type paper shot shells had a wax on them and the wax melted and coated the chamber. This actually protected them, and people weren't prepared for the chamber rust problem of plastic, which burns off any wax or oil.
The chamber cleaner brush is soaked with solvent, pushed into the chamber and the rod handle is used to rotate the brush.
This scrubs the fouling out and leaves a clean, smooth chamber.
For rifles, you really need to buy rods for each specific rifle, unless you have a number that are the same general caliber and length.
As example, if you have an M1 Garand or an M1A you should buy a stainless "Service Rifle" rod. These are rods that are the correct length to clean these rifles from the muzzle and not contact the open bolt.
If you have a very short carbine type rifle and another rifle with a longer barrel, it's easier to have a rod for each length just because the longer rod in a short barrel is awkward to use.
You don't have to have 10 rifle rods stacked up, but try to have the right rod for the rifle. If you can get by with a rod for a number of rifles and it works well, that's fine.
I do NOT recommend any kind of "pull through" cleaners.
Bore snakes are for fast field partial cleaning and don't get a bore really clean.
The problem with the bore snake is that people wash them and use them far too long.
The material gets weak, and sooner or later it'll break off in the bore.
The smaller the caliber, the more likely this will happen.
If you break one off in the bore, there is no good way to extract one.
One person on the forums a year or two ago broke one off in an AR-15 , tried to pull it back out and broke the other end off.
Last I heard, he still hadn't been able to get it out.
The manufactures will tell you they don't have a good extraction method to recommend.
The Otis is a nice kit, but as good and high quality as it is, it too can and will break off in the bore.
Nothing cleans as good as a rod and patches, and rods don't leave things jammed in the bore unless you mis-use it.
Rod tips are a matter of preference and the type firearm to be cleaned.
I use both loop jags and button tip jags, all made of brass.
I don't recommend plastic jags. They strip the threads and break.
I've pretty much stopped pushing rods through bores. When you push, the rod flexes and bumps the bore. This may not do any harm, but after I saw rifling impressions on a rod, I started pulling the rod whenever possible.
When I can clean from the chamber, I still use a loop tip and pull the patch or brush.
The only down side is you have to be careful not to pull a bunch of dirty solvent into the action.
The purpose of a patch is to carry clean solvent into the bore, and dirty solvent out.
"Pumping" a patch up and down the barrel does nothing. It doesn't "polish" the bore and it doesn't scrub off fouling.
I put patches through the bore and out the end on one smooth pass then pitch them.
Buy brushes in bulk from Brownell's or Midway. Solvents eat the brush and they don't last long no matter what you use.
To make them last longer, rinse them off with cheap paint thinner or alcohol to remove the solvent.
When a brush feels like it's not as tight in the bore, pitch it.
Solvents need time to work. A solvent works by a chemical reaction with copper and carbon fouling and that requires enough time to work.
READ THE BOTTLE LABEL for how long your solvent can be safely left in the bore.
Hoppe's Number 9 can be left in for weeks.
I use Hoppe's in this method for a rifle.
I run a brush soaked with solvent through about 10 to 15 times.
I run two soaked patches through, then let soak for 30 minutes or so.
I soak a clean patch and run it through in one smooth pass. When it comes out the end I look for blue or green stains, which indicate copper fouling is still present.
If I see signs of fouling, I let it soak another 30 minutes and check again.
I continue this until I don't see any stains. Then I dry the bore and put in a very thin coat of CLP Breakfree.
A day or two later, I wipe the barrel dry and run another solvent soaked patch and let it soak for 30 minutes. This is to insure I got all the fouling, including any that works it's way out of the rifling corners later.
If I have a bolt rifle and it's been fired more than 20 rounds or so, I brush the bore, run two wet patches, then I use a Brownell's chamber plug to plug the chamber. Then I fill the barrel with solvent and let soak 24 hours.
I then discard the fouled solvent and dry.
This only works on rifles that don't have a gas port in the barrel, or one like the M1 that has the port near the muzzle.
Since pistols don't normally get copper fouling build up like rifles do, these can usually be cleaned in an hour or so.
I do have a Kahr Arms pistol that gets thick layers of copper fouling in the polygonal bore, so for it I either use JB Bore Paste, or I put the barrel in a tall, thin container and fill with solvent. I let it soak at least 24 hours and if it's been shot a lot, I may dump the solvent, refill and soak longer.
A good "tool" to have for cleaning is a small plastic solvent transfer bulb or pipette.
Use this to apply solvent to patches and brushes and this prevents contaminating the bottle of solvent.
You can buy pipettes from lab supply houses, or from Brownell's.
You can put a patch or brush into the bore, then apply the solvent with the bulb.
So, since there is no really good "universal" cleaning kit, most of us build our own kits, using a tackle box.
Buy whatever one-piece stainless or carbon fiber rods you actually need. You don't need a rod for each gun, but if you have an accuracy rifle you may want a rod just for it.
Buy brass muzzle guides for any you have to clean from the muzzle.
You may want to look at chamber guides for rifles that are cleaned from the chamber. These keep solvent and dirt out of the action.
Buy jags of whatever type you like for each caliber. Some will do for more than one, as example 9mm and .38/.357.
Buy plenty of bronze brushes for each caliber.
Buy a good solvent of whatever you like, and buy it in the largest size you can get. Transfer it into smaller jars to prevent major spills.
Buy some pipettes.
Buy any extras for specific firearms.
As example JB Bore Paste for badly fouled bores, Slip 2000 Carbon Remover for carbon fouled gas pistons or muzzle brakes, a lead-removal cloth to clean carbon and leading off stainless steel revolvers (NO use on blued), if you have a revolver buy a Lewis Lead Remover kit from Brownell's even if you only shoot jacketed bullets. The Lewis kit also removes carbon and copper buildup off the forcing cone.
This sounds like a lot and sounds very complicated. It's not because you buy all this over the years as you need it.