I use a combination of Pro Shot SS, Dewey SS/coated and a few old Belding & Mull SS Rods. I don't use the coated Dewey rods with TM bore cleaner, it eats the coating!

when/if you break one,
If you break or bend a rod you need to re-evaluate your jag-patch combination. A patch-jag should be pass through a bore with light resistance, it's only job its to remove what the solvent has dissolved. In short solvent eats it, the patch removes it. Also just because the packaging says "X" bore doesn't mean they're right especially when mix and matching brands. For the most part I use Pro Shot patches but I have made jags to fit others and sometimes I'll use a 24 bore jag in a 25 bore. It all depend what fits.

Speaking of solvents, I suggest using Wipe Out and or Gunslick foaming cleaners. Although I use Butch's and TM I find myself using the foaming cleaners in the shop more often now days.

Maybe I should have said that I intend to also get the bore guide system with the rod brand and I use
Lucas bore guides are the standard ($$$) although something is generally better than nothing. The bargain basement type MTM guides are pretty much one step below worthless. The term "bore guide" is a bit misleading, its really a rod guide to keep the rod centered going in and out of the throat while the patch keeps it centered in the bore.

While were' on the subject of cleaning, anyone know this gadget is used for?

I should be used as part of your cleaning regiment along with the bore-chamber.

Bill