Here is your gun, as I recall the frames of these-(the original ones, I think the originals also had a round bbl. to save on cost and production time)were made from brass alloy that the Rebs melted down from some famous set of church bells, the guns were nicknamed in honor of the church. Something I read years ago and can't quite remember the details.
http://www.cabelas.com/prod-1/0006186210086a.shtml
For a good cleaning, I just disassemble the revolver and plop the parts in a pan of warm soapy water and scrub them with an old tooth brush. Dry them and use another brush to apply lube, you can use bore butter or make something similar. I find it takes about the same ammount of time as it does to clean a modern revolver shooting smokeless. Take a S&W 586, to really clean one well, you have to spend alot of time brushing out the cyclinder ends and chambers, the frame crevases, and of course the bore. Because you don't dissasemble it, you need to be carefull that excess cleaning fluid does not go in the action. The crud from smokless is harder to remove that BP, It takes quite a few patches with shooterschoice to get a smokless bore perfectly clean(especially when shooting lead), but only a 2-3 do the trick with soapy water on bp. The only real difference is that with a BP revolver, you need to clean it fairly soon after shooting and a smokless one can wait quit awhile.
For a quick cleaning of a BP revolver, especially if you plan to shoot it again anytime soon, try Go-Jo hand cleaner-(without Pumis). This stuff reallycuts the crud, does not get all over and in the action like a liquidand the lanolin in it leaves a little bit of moisture barrier behind that delays oxidation for the short term. I just do the bore with Go-Jo and grease it. The cylinder and frame get done with a brush and wiped with a rag, if you greased the nipples before you installed them then they won't rust in place very fast and the smaller parts in the action should have been greased after your last good cleaning so they will be fine too. I generally take mine out 3-4 times befor a complete cleaning, depends on the timeframe and amount of shots fired.
The cylinder pin on the Rems do not have grease grooves but by using a good lube on them, you can get 6-8 cylinder loadings befor cleaning is required. Just use a grease that will not get too stiff in winter and another one that will stay put in the summer heat. I vary mine by the amounts of bees wax I mix in.
Those felt wads do a decent job of preventing chain fires and have the added benifit of cleaning the bore somewhat. Putting lube over the balls also helps to prevent chainfires but it really aids in keeping some lube on the cyclinder pin and also in keeping the bore fouling softer. I've found that a little cream-O wheat over the powder does the same as a felt wad, is just as easy to put in and costs almost nothing. Just put some in an Old mustard bottle and squirt it in after you charge the chambers. A little practice and you will be able to get virtually the same amount in each chamber.
Enjoy your new gun, keep the loads on the lighter side since you have a brass frame. A guy who worked for me had one and it shot great, really good as I recall.
Doug