Are you sure it's a Renegade? It sure looks like a New Englander. If the barrel is round, it is a New Englander, another fine rifle 1:48" twist. Be careful with the bore brush and bore mop. I only buy the style that loops the wire through the brass. If it is only twisted wire glued in, they have a bad tendency of falling off. I wouldn't worry too much about using either one anyway, you don't really need a bore brush. I use one once in a great while to get into the chamber of the patent breech. you can google pictures to see what that looks like. They used to make a scraper just for TC's, but the brush works just as well. I might do that once a year. Water and a patch is all that is needed to clean black powder. With pyrodex, a little soap wouldn't hurt.
Pyrodex works, but is not the best powder ever. Make sure you clean the rifle immediately after firing. I wouldn't let it sit more than a few hours, or whatever the drive is home. If you let Pyrodex sit overnight, you will find a rust bucket in the morning. A blackpowder like Goex or Swiss is ideal. You still need to clean it eventually, but a rifle left overnight as you gut and skin an animal is just fine. I've even hunted 2 days on a fouled bore with no rust with black powder.
I would not waste time with the Lee REAL bullet. I've had 5 TC guns, and the REAL is horrendous in all of them. The only guys who get them to work seem to have tight bores. TC is pretty consistent and true to size. A round ball is a great choice. A maxi ball is usually very good as well. The other two tools you will likely want is a patch worm, and for sure get a nipple wrench. A ball puller is not a bad idea either. You will dry ball eventually, it's just a matter of when. The easiest cure is to unscrew the nipple, trickle as much powder as you can through the hole, put the nipple back in, and fire. Boom, barrel cleared in 2 minutes.