You certainly don't need an expensive kit to clean your rifle. Track of The Wolf has everything you will need
https://www.trackofthewolf.com/List/Category.aspx/558 What you will need are a good solid rod. I don't like the jointed rods because they are prone to coming apart or breaking at one of the joints. A cleaning jag, a bullet pulling jag, a nipple wrench, some patching material (old T shirts work just fine), some dish soap, a container to put the soapy water in, and some elbow grease. I also use some WD-40 after cleaning and rinsing the bore just to get rid of the last traces of water. Finally some good oil such as a gun oil or some light machine oil such as 3 in 1. I never use a brush on my bore because a brush can get stuck and be a beast to get out.
Before you start any cleaning, check to be sure it is not loaded. Do this by putting your rod down the bore and marking it at the muzzle. Then remove it and lay it alongside the barrel to see if it reaches the breach. If it is short of the breach, there may be a load in the barrel. To remove a load, you will need a bullet pulling jag on your rod. It looks like a wood screw. Use a good bit of force to screw it into the ball in your bore and then get someone to help you hold the rifle while you pull on the rod. It isn't an easy task and may likely require several tries before you successfully get the ball out. Whatever you do, do not try to shoot it out because you do not know what the previous owner has loaded it with. He could have loaded it with modern smokeless powder and that will be like a pipe bomb.
To clean your barrel, remove it from the stock and remove the nipple. Put a bit of dish soap in your bucket and add some warm water. Put the breach end of the barrel into the bucket and start pumping a wet patch up and down in the bore to flush it with the soapy water. Do this until the water coming out of the nipple hole looks clean. Then remove the barrel from the bucket and rinse with clear water. Run several dry patches through the bore to dry it and then spray it with WD-40. Next, wipe out the WD-40 with some dry patches. Wipe the bore with a patch moistened with oil and you are done. Clean out the nipple and dry it. Put a dab of grease on the threads of the nipple and replace it. This procedure should have your bore nice and clean and ready for inspection. I don't think I have missed anything but if I have, one of the other folks on this forum will catch it and straighten you out on the procedure. Good luck, those Renegades are pretty darned good rifles.