If you want to do this once and once only my suggestions would be;
- Handguns have such a short barrel that I use a three piece rod with the jag and brushes on each piece instead of joined. That speeds things up by not having to swap the ends for each step. The short barrels have so little twist that it's not an issue. I just let the rod rotate in my grip to follow the rifling.
- For guns you must clean from the muzzle ALWAYS use a crown protector. These can be plastic or brass but after using a few options my favorite is a stainless rod with a brass cone protector. The smoother operation of this combination makes it easier to use
- For brushes I prefer a nylon bristle brush for normal cleaning and only using a bronze bristle brush for seriously stubborn deposits such as any leading I may find.
- A proper fitted cylindrical jag does a far better job of patching the bore than the eye loop style. A set of Tipton jags has proven to fit all my various size bores very neatly.
I prefer to sneak up on cleaning. So I start with just patches. If that's not enough to make it really clean I run the nylon brush with some solvent on it for a few passes then patch again. If it's a gun that shoots cast and it's still crusty in the edges of the rifling I run the bronze patch a few passes then patch. Usually I don't need to though.