I've never bought a "kit".../ too many accessories in a "kit" that kind of look useless.....so I've just accumulated:
A good pistol length cleaning rod ( I like one piece / coated rods ) I think they're vinyl or Teflon coated..not sure what brand. But I like them with larger handles vs smaller handles. I would not use uncoated steel rods.
a bore brush...( I prefer bronze bristle brushes over nylon) Otis is a good brand.
solvent of your choice ( I like Shooter's Choice)...but there are lots of them out there now...even Hoppe's ...Gun Scrubber, GunSlick, Tetra...and on and on.. For a spot that won't come out of a bore...I use Barnes CR-10 ..copper remover...
a few patches ( I use 12ga patches for most everything - you can cut them with scissors - or just put the rod at one side, and use them in everything from 9mm - .357 mag ---.44 mag ---and 12 ga...) ....cotton flannel is what I buy..../ and I only use a couple of patches per gun - and 3 or 4 paper towels.
and some kind of lube ( I like Break Free CLP ).../ where I want a lighter oil, like on a firing pin spring, I will use a spray can of Rig Oil #2. If I want to use grease...I'll use Rig Universal Grease...or Wilson Ultima Lube...( I've tried a lot of other stuff ...and keep coming back to these !
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I also like "Bore Snakes" ...they make a really good product / especially for revolvers, where you really shouldn't clean from the muzzle end of the barrel. I use the same chemicals....bore snake just replaces the rod and brush.
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I have a cleaning mat on my workbench...( if you don't want a mat - then use an old bathtowel )...and I keep a small 4" X 6" box on the side of the bench....with patches, some Q tips, couple of old tooth brushes, bushing wrench.....cleaning stuff, lube and oil stays in another box...so its not just scattered all over / if I need that bench area for something else, I could put the boxes on a shelf / pickup mat...( but I don't )...