Howdy Pard!
Check out my pics on the hat thread; I've been doing what you plan on doing! I started just under a year ago shooting duelist cap and ball pistols at SASS matches (Frontiersmen class, which requires cap and ball shot duelist). (I had been doing duelist BP cartridge for a decade prior). No disrespect to Mako, but I would not recommend starting out with gunfighter cap and ball! (Master gunfighter with cartridge and duelist cap and ball first, then think about combining them!) I, too, use a Henry in 44-40, or a '66 carbine in 44-40 (depending on how strong my arms are feeling that day!). For shotgun, I use either a Rossi hammered 12g or a Zabala hammerless 10g double.
As for me, when I started with C&B, I figured reliability was key. I changed out to Treso nipples and Remington#10 caps, and then took my pistols to the range (Remmies and 1860s) and made sure each pistol would go 30-36 rounds without any significant intervention. (No disassembly, major relubing, or cleaning etc.) It helped to prep the entire pistol with straight ballistol, use copious amounts of bore butter on the cylinder pin and notches, put wonder wads over powder with extra bore butter on them, clean out any lube from the nipples and wipe out the cylinder chambers the night before, clear the nipples at the range before the match, etc.
I then practiced dealing with cap fire without chamber ignition (it will happen on the line eventually!) I made sure I had extra caps on my person (either in a capper or a cap pouch lined with sheep skin), a small knife that I could get to with one hand (to take stuck dead caps off nipples) (neck knife/patch knife works fine!), a nipple pick, and small cap seater (dowel rod with leather covered tip or a piece of #2 pencil with eraser on it (not PC but very portable and it works!)).
I also made sure all my gear fit me, was comfortable to wear for hours at a time, and securely did whatever it was suppose to do (hold guns, caps, 10 rounds of spare 44-40 ammo, etc)
As for loading the C&Bs, I decided to go with just what I thought was needed and no more. This all fit in a nice leather possibles style bag (which I do not carry to the line). This held a powder flask with spout, ball bag, larger leather tipped dowel rod style cap seater, tins of caps and wads (enough for an 8+ stage match), small rag, 2 spare nipples, and nipple wrench. I also use a cheap wooden loading stand. (I do not remove the cylinders from my pistols to reload them, and I do not use multiple cylinders for a match; only the one that came with the pistol. I don't want to have to clean all those extra cylinders and nipples!) I tried to keep things period correct looking when possible, but am not a slave to authenticity.
All this has worked out well for me, with hardly any changes since I started. If you'd like to ask me any questions, please feel free to contact me!