I started shooting CAS about 3 years ago. I began with a borrowed 1897 Winchester Commemorative in 44-40. My next rifle was a Cimarron '66 Yellow Boy in 38 Spl. Followed by a Miroku 1873 in 38/357. I've got a short stroke kit and light lifter in the 66, but I run the '73 mostly. The Miroku is stock, cleaned and oiled was all it needed, except I tightened the mainspring a touch. If the mainspring is too loose the rifle flings the empties too aggressively. Too tight and just pop out.
Most miss fires come from over running the rifle. Operating the lever before the hammer has struck the primer.
Henry has a heck of a warranty, I think you'd be OK with one. They have different models of Big Boys, and they all load through the tube. This may be an issue at the loading table. Loading is a bit easier with a side gate, IMHO. A fellow shooter has one in 45LC, and he seldom uses it, says he should have got it in 38/357. Unless you want to shoot Wild Bunch as well, it's a pretty popular choice of calibers.
A Marlin 1894 in 38/357 works fine, but expect that you may have to completely take it down and clean out the metal filings and grit. I had an 1894 Marlin in 44 mag, it didn't pass load development, so I sold it. I'm not a fan of their extremely slow twist rate and shallow groove rifling. Marlin "Ballard" looking rifling is just Mircrogroove with 1/2 as many grooves, certainly not deep cut Ballard.
Marlins will run for a long time before they wear out and start doing funky stuff. The lifter and magazine cutoff timing gets a bit wonky. Don't let that scare you off if you like the rifle, pretty much any of the levers will end up at the Dr at some point. The '92 is probably the only one that stands up to the punishment, but they are not as fast as a '66 or '73. Unless you can do basic gunsmithing, stay away from a Rossi '92.
What caliber are your hip guns? Do you want to run just one ammo? Do you handload? Hip guns can eat any sort of ammo, as a rule. Lever rifles can have fussy appetites. Even though I have 357 hip guns and 38/357 rifles, I still have different ammo, it's a long story, bottom line I'm a bit anal when it comes to accuracy and performance. Shooting CAS doesn't need that good an ammo.
My '66. '73 and my sons '92, a Rossi in 44 mag.
The Marlin I did not like. Shame, I spent several hours cutting the checkering. It comes lazer burnt, not nice.
It does cut into some decent checkering, you can't remove all the charcoal, but most of it is gone.
Take care and if you can't decide, go to a meet and if where you shoot is like our matches, you can always borrow a gun or 2. I borrowed a shotgun and a rifle from a relative for my first meet.
Which shotgun are you planning to use? I got hooked on the '97, a SXS is a good choice, but again, just not as fast.
Nitro. (AKA Big Boston, for CAS)