I have the Tipton brass jag kit. I prefer to use Butch's "Triple Twill" patches. None fit. So I am usually using, for example, a 7mm jag in a 30 caliber rifle with patches described as 1 3/4" for 7mm to 35 cal. Or a .243 jag in a 6.5mm rifle with 1 1/2" patches described for 6mm/243 Bench Rest. Down at the very bottom size for me, the .224" rifles, I chucked up that jag in my lathe and reduced its diameter so I can use the 1 1/8" square size for 22-270 cal. So four sizes of patches, and 11 jags seem to take care of .22 through to .458. I do not have a cleaning rod small enough for the .17 jag, but do not have rifles in that bore size either, so it just sits in the box - has a smaller thread size than the rest.
I often also use the nylon bore brushes - wrap a big patch around the long way, soak in "juice" and do full length strokes within the barrel - had read to NOT reverse direction with a brush within the bore - so all the way through one way, then all the way back out. Seems to provide a bit more surface, and bit more "scrubbing" than just a patch on a jag. Watch about the rotation - if your patch, brush or swap is fitting well, the rifling may be unscrewing it from the cleaning rod, and do not really want it to come undone partially down the bore.
Really nasty bores will get a scrubbing with the "Tipton Best Bore Brush" - package says they are brass wire. I goop a lot of RB17 Gun Cleaner on the brass brush - it is like a gel, so seems to get most into the bore. I have found that the "brush" gets "worn out" in less than 100 full length strokes - significantly less resistance than when new, within that bore, so I buy them in packages of three from Amazon.ca. I am usually much too lazy for this, and prefer to use WipeOut and leave the thing soak overnight - often repeatedly, but I have room in my shop to be able to let a rifle sit in a cradle as long as it needs to - others may not have that space available.