I prefer uncoated steel rods, so I still use the Kleenbore kit I've had since Kleenbore went into business. I still use the Formula 3 , No. 10 and Copper Cutter solvents by Kleenbore. The muzzle guard is important when cleaning form muzzle.
I also still use the Otis Kit had it for a good while also. I have bought the components (different calibers, pistol rifle...) as I will often just have that in range bag, back pocket afield, range.
This is also the reason I don't have a boresnake...they are fine, its just I've owned the otis for so long and fits anything from .22-12 ga...and I don't have to wash the snake. Also one cleans from breach--the preferred method. If you later get a revolver, or a lever action you will see advantage.
Tackle box, mine has the deep storage on top, and drawers underneath. Extra components, tools, parts...
Long wooden Q-tips, pipettes, applicator brushes ( Radio Shack, Hobby/Craft store), pipe cleaners, double ended nylon brushes...and save your old toothbrushes, from NAPA get the nylon cylindrical brushes, avail in .22 - .45cal.
( pipettes use for solvents, and tranferring lubes into smaller bottles...keep things safe and non contaiminated.)
Caveat: Careful getting a bunch of different products and mixing them...some do not mix and can cause harm.
Isopropyl alcohol, and Zippo lighter fluid...oh yeah almost forgot...
RIG Grease to protect externals.
I given so much stuff away , its easy to get caught up, when you win this stuff, in a shooter's kit or gifts...just keep what works and save money for ammo, mags, lessons.
NAPA Breaklean is cheaper than Gunscrubber btw