Glad to hear you didn't have a bad experience with #13 like I did.
For me, using the #13 cleaner created instant rust.
The bore rusted before I could even get a clean wiping patch down thru it.
Never again will I even allow that stuff in my house.
I think after a bit of shooting and cleaning, you'll find that plain old water works just as well as any of the modern "bore cleaners".
If you've been shooting something with any kind of oil or grease on it, adding a few drops of dish washing detergent to the water will be all that's needed to clean the gun.
Besides fully drying the bore, perhaps the most important thing to do is to apply a good anti-rust gun oil to the barrel.
I like Barricade but there are other good products that will work OK.
When you are oiling the barrel remember, if any of the oil runs down inside the small hole in the breech, it will lay there waiting to contaminate the new powder charge the next time you load.
Oil in the powder will prevent it from igniting so be careful about using too much.
Actually, many shooters store their guns with the muzzle pointing down.
They do this to keep any excess oil from collecting in the breech and in the hole that connects the breech to the nipple (or vent).
Have fun. :thumbsup: