Don't overthink it - it is actually pretty simple:  Waster will dissolve BP fouling, so you can use water to clean out the fouling.  Run a couple of moist ptches through the barrel, followed by a few dry ones - after all, you don't want to leave H2O in the barrel..
Just water will work, some people use a water/water soluble oil solution (although this is most frequently for wiping between shots).
Then you can just oil your barrel to protect it.
If you have leading, 1st clean out the fouling, then go for the leading with whatever your favourite recipe is.

I actually clean at the range - few wet patches, a few dry ones, and 2 oiled ones (I use Ed's Red) - that's all that is usually needed.   
Nornally there is no need to brush the barrel, and running water through the barrel is way overkill, with the risk of getting water in the action - not good...

Now, the cases do need a bit more work though!

Geez Roscoe! Waster is wader wit wader-salable oerl.  I taught anibady new dat. . It be much more betta dan regalar wader.

Damp patch, back and forth a bit.  Then another untill it gets a bit cleaner.

Then patches with bore cleaner on them, I use Ed's red on everything.

Do it again the next day to be sure.

It really is not rocket science.

First, I do wipe between shots, and at end of shooting.
For gg bullets, wipe twice between shots with dist water.
for PP bullets wipe twice dist water patch, then 
1. 2-3 patches wet with Windex with Vinegar(NOT Ammonia)
2. Dry patch
3. Patch wet with 99 % rubbing alcohol(remove water)
4. Dry patch
5. Patch wet with Olive or Canola oil.
Next time shooting, simply run 1 dry patch thru bore, and ready for first shot

my cleaning process is glass cleaner, w/vinegar and water [50/50 mix] when patches look clean, dry bore and run a damp patch of balistol to coat the bore and all the metal surfaces, been working so far

Popes instructions to clean a barrel were quite simple: I use nothing but a drill rod (smooth tool steel) cleaning and proceeding as follows. 
1.      Always clean from the breech never the muzzle end.
2.      I always use absorbent cotton for cleaning my barrels. Pull out a tuft, which will be a rather tight fit in the bore. Place this on the button head of the rod; use it dry and push it clear through the barrel thereby pushing out nearly all the dirt. You don’t want to use any fluid on this and make a solution of powder dirt that runs all over the gun. 
3.      Take another piece of cotton almost as tight and wipe this back and forth a couple of times. Turn this inside out and do it again.
4.      Take another piece not so tight and wet this with Hoppes #9 powder solvent, wipe back and forth two or three times, turn it inside out and repeat. 
5.      Take another piece of cotton that will fit very easily, wet this with Hoppes #9 and wipe back and forth so as to leave the barrel swimming with it. I have used Hoppes #9 practically exclusively for 27 years and I have never had a rusted barrel. It plays no tricks, there may be something just as good BUT LET GEORGE USE IT. 
6.      Take the same piece as in number 5 and wipe out the countersink of the muzzle and the muzzle of the gun then around the breech and action, and put it away it is safe.

This is from Respectfully Yours H.M. Pope.

40 Rod

There you have it. Lots of options.  Every shooter has at least 2 ways.  Surprisingly, they all work pretty well