Well now that you are a revolver owner you must reside yourself to the fact that revolver cylinders get burn rings on them - period. You can clean them fairly thoroughly with a copper brush and Hoppes #9 but you are wasting your time. Cleaning every last bit of the burn marks off is futile because the very first time you shoot 6 rounds they will return. What is important is that you clean it well enough to just keep the burn marks from getting a thickness build up. If that happens then the cylinder rotation and function can be impeded. Over cleaning the cylinder face can cause more problems that it is worth and all you want to do is clean enough to keep build up from occurring. A working revolver (once it is fired) and fired on a regular basis will always have cylinder face burn marks and as long as the revolver is not to be a "Safe Queen" that is perfectly acceptable.
I find that G96 Synthetic CLP works the best of any CLP I have tried. Break-free CLP is also a very good product but IMO the G96 synthetic does clean a little better - lubrication and rust protection qualities are the same for both. That said, the best cleaning solvent of all is Hoppes #9 which is what you can start with. After you have cleaned the face enough, use CLP for the rest of the revolver. The powder marks and soot usually wipe right off with CLP.
HINT #1: Get yourself a piece of 18" x 18" piece of 100% cotton flannel and drizzle your favorite CLP all over it. Stick it in a plastic freezer bag and the CLP will evenly distribute itself all over the rag. That is now your range rag and use it to wipe down the handgun or rifle immediately after shooting it. That will remove the lion's share of the dirt, soot and gunk so when you get home, cleaning it will be so much easier. Most warm guns clean up much better and faster than they do after sitting for hours. This process should take 30 seconds and is only required to get the heavy stuff off before re-casing the gun. I have done this for 50 years and do it every single time I shoot any gun. Most of my friends have seen me do this and have followed my lead. The range rag can be used for a year, adding a little oil when needed. When it is very dirty simply toss it and make an new one. I usually have a bunch of latex disposable gloves with me that I also use as I am not wanting to get lead and powder all over my hands.
HINT #2 Make up another rag and use it for only wiping down a gun prior to putting it back in the box for storage. This removes all finger prints and insures the gun will remain rust free while stored. Dedicate this rag for this purpose only. It need not be dripping with CLP, just thoroughly and evenly coated. I usually buy about 5 square yards of white 100% cotton flannel at a fabric store and this lasts me years and years. I like white because it allows me to visually see how dirty the rag is. You don't want to clean off a gun's finish with a really grungy rag! Cotton Flannel is not expensive. Oh - I also use very heavy duty freezer type zip lock bags to store the oil rag. They seem to last a good long time. Do NOT wash the rags!!! Toss 'em and start fresh. You do NOT want all the junk in a clothes washing machine and you do not want to wipe your guns down with residues of laundry detergents.
