There is a lot of good advice given in the posts, but I don't think it needs to be so complicated. Although I only shoot flintlock, I can help you some.
First, pulling a ball with gun powder under it can be dangerous. Use Alden's suggestion and get a CO2 gas discharger for expelling balls from the muzzle. Be sure the muzzle is pointing in a safe direction, as the ball is usually expelled at considerable force. Unscrewing the nipple and pouring 4F powder into the bolster is also an easy way to expel a ball from the muzzle. A lot of shooters carry those brass 3-grain primers (Track of the Wolf) in their shooting bags for such occasions.
You did well to thoroughly clean the preservative grease/oil from your new rifle's bore before taking it out to the range. But if you put petroleum-based oil down the bore to protect it, then that too will need to be thoroughly cleaned before your next shooting session. Use a good solvent, like brake cleaner. Before loading the rifle for the first time at a shooting session, step up to the firing line and snap-off a couple of caps to clear the patent breach. Hold the muzzle down close to some grass or other vegetation. If the patent breach is clear, the caps will move the grass blades, even kick up a little dust.
Some clean the bore between each shot when target shooting, while others will only clean when it becomes noticeably difficult to run the patched ball down the barrel when loading. When cleaning between each shot, use a damp (not wet) patch and run it down and and back out the bore only once. Don't pump it up and down, as that will only push the fouling into the patent breach and plug it up. Keep a small bowl of water nearby, as the patches can be rinsed out and re-used all day long.
I see no reason to put anything on top of your powder before running the patched ball down. Some do it, but most don't. Experiment with your patch and ball combination to find the best combination for the level of accuracy you want. For instance, many use a .490 ball (50 cal rifle) with a 0.015 inch patch, while others like a more looser fit wherein they can start the patched ball down the muzzle with their thumb and finish up with the ramrod. Others use a tighter combination that requires a short starter, or even a mallet, to get the ball into and part way down the muzzle. But experiment to find something that is comfortable for you. There is no rule for a proper ball/patch combination. Just avoid burning holes in your patches (collect a few after firing your gun for inspection). Remember, though, a new rifle will tear your patches for the first 100 or so shots, or until the cut rifling's sharp edges are smoothed off. If holes are burning in the patches, the patch/ball combination is too loose. Tighten it up with thicker patching material. I like Bridgers Best patching. Don't get it or any other brands that are prelubed, as those packages often have sat in distribution with the fibers beginning to deteriorate. There are good lubes on the commercial market, while others use their own concoctions such as animal fats with added bees wax. Patches soaked with saliva also are good for target shooting where you are loading and shooting; not for hunting or trail walks, use an animal or plant grease-based patch lube to avoid rust-rings where the patched ball has sat. If you get lost for a few days when hunting, you can subsist on your patches until rescued. Me?...I have never been lost in these shining mountains but I have been confused for 2 or 3 days at a time.
After a day of shooting, remove your barrel from the stock. Remove the nipple and place the breech end in a pail of cool or tepid (but not hot) water several inches deep. Some add soap or dish detergent, but it is not necessary as black powder fouling readily dissolves in plain water. Use your ramrod with a cleaning jag and patch to pump water in and out of the barrel. Change the water several times or until further pumping a patch no longer shows dirty water. Dry the barrel thoroughly with dry patches and use a bore preservative to protect your bore. Barricade is popular. Don't forget to spray a little into your bolster from the nipple end, and, as on individual suggested, store your re-assembled rifle muzzle down to avoid oil from pooling in the bolster or patent breech. Don't forget to put a cloth under the muzzle when doing so to avoid any matrimonial conflicts.
Don't take your shooting too seriously; remember to always have fun, while being safe.
George
