Welcome aboard! You've got a fine rifle rifle in that TC Cherokee, and the .45 cal itself is a real winner. Probably my favorite all-around caliber for eastern hunting. It can be loaded light for small game and still be very accurate and with a stepped-up powder charge, is more than powerful enough for deer. That applies to many other calibers as well, but I've found the .45 to be almost perfectly balanced in this regard.
The .440" round ball would be my starting point too, and Al's recommendation of an .018" patch should work fine. I've been doing quite a bit of experimentation with patching and lube this year and am finding several different approaches that work well. A loose, easy-to-load patch seems detrimental to accuracy, as does one that's overly lubricated. When using a ball/patch combo that is "somewhat" difficult to load and just a little damp with lube, I'm seeing my groups really begin tightening up. My main rifle (an early Lancaster .45) seems to like a spit patch best of all.
I would recommend using real black powder, as I find it much easier to ignite and the fouling to be much softer and easier to clean than any of the substitute powders like Pyrodex, Triple 7, etc. I shoot Goex FFFg in mine and am at want for nothing in that department. Regardless of what powder you use, ALWAYS clean your rifle thoroughly after shooting! I'll run a cleaning patch through mine the following day (after a thorough cleaning) and then again a few days after that, just to ensure the bore is clean. Any rust or darkening on the clean patch indicates the rifle needs additional cleaning.
Good luck with your Cherokee, and please let us know how things work out for you.