Often, "the best" depends on the type of firearm you're cleaning, but here are some basics that I believe are common to all cleaning tasks.
Cleaning Rod - to properly clean a rifle, shotgun, or pistol barrel, you absolutely must have a rod made in segments or specifically made in fixed lengths for just about any barrel you are working with. Most rods are made of brass, carbon fiberglass, or stainless steel. Some are coated to protect the finish and rifling in the barrel. Some rods made specifically for shotguns are made from rosewood. Stay away from aluminum rods. If possible find one with a free-swiveling handle.
Cleaning Brush - These are stiff spiral brushes with a threaded end so that it can be attached to the cleaning rod. They are commonly made with nylon, brass, bronze or stainless steel bristles and are primarily for scrubbing the inside of the barrel to remove carbon, lead, and Brass fouling left behind after a firearm is shot.
Brushes come in a wide variety of sizes, so make sure you get the right brush for the caliber or gauge you are cleaning.
Jag - Jags are brass plugs that attach to the cleaning rod and are used to push cleaning patches through a scrubbed barrel to remove loosened fouling. They are made for specific calibers and gauges so, as with brushes, make sure you get the correct caliber/gauge for the firearm you are working with.
Cleaning Patches - These are small cloth patches made of lint free material used together with Jags to push out fouling. Make sure you use the best size patch for the size barrel you are cleaning. I recommend:
3 in. x 3 in. for shotguns
3 in. x 1.5 in. for .30 to .45 caliber
1.5 in. x 1.5 in. for .243 caliber to 7mm
1 in. x 1 in. for .22 caliber
.75 in. x .75 in. for .17 caliber.
Pipe Cleaners - For cleaning those nooks and crannies your finger just won't fit into.
Simple Green Spray cleaner. I know , I know...you didn't see that in Bass Pro Shop. But it is biodegradable and it degreases and loosens carbon fouling every bit as good as (and a lot cheaper than) stuff sold specifically for cleaning firearms.
Lubricant-Cleaner-Protectant (LCP) - A synthetic product made by many manufacturers used for oiling metal parts after they have been cleaned.
Silicon empregnated cloth for wiping down your firearm before storing.
Lint free rags.
These are the basics I recommend to do a thorough cleaning of any firearm. They are fairly inexpensive and absolutely essential to keeping your rifle, shotgun or pistol in good working order.
In future posts, I'll focus on HOW to use these basics to clean a firearm.