Most people will steer you towards the Marlin, and justifiably so, and I'm one of them. Marlin makes a fine rifle. That said, there is a rather large group of shooters who feel that the older "JM" marked levers are by far the best. I can't say that with the same effervescent enthusiasm. I recently bought an 1894C ("JM" marked) and a new production 1894CB made by Remington. Both are .357mag. The fit and finish, smoothness, reliability. and overall quality of the newer one far exceeds the older one. The older ones do command a premium, and many hold out for those.
Keep in mind, my assessment is based on a sample of one each. I owned several Marlins back many years ago and never had any complaints. They have always been a meat and potatoes, working mans rifle. It is quite possible that my older Marlin was built on a Friday, the day after a big party at the plant. Conversely, my 1894CB may have built on a day when they announced an inspection by the big dogs of the Remington company and everybody at the line was on their toes that day. A set of Skinner sights, a decent sling, a few thousand rounds of good ammo, and I'm a happy guy.
There's nothing wrong with the older 1894C at all. Fit, finish, and all the parts and pieces are just fine and the rifle is smooth and accurate. It was very lightly used and not a mark on any screws. Very little wear on the bluing inside and out. It's a great rifle, I've got no complaints. Very happy with it. It's just that there's a noticeable attention to detail of the newer one. It's tight, smooth, nicer wood, and very accurate. Surprisingly so.
I've heard so many times that the "JM" marked were so much better that maybe my assessment is a little skewed. I did have very high expectations. But I'd trade my "Much Better" "Real Marlin" "Built with old world pride" straight across for a junk "Remlin" 1894CB in a hot N.Y. minute. And that includes the upgraded springs, metal follower, Skinner sights, and my own fluff N buff. I'd do it and never look back.
Many here have given you some great advice. Almost any of the rifles recommended can be slicked up and be a great shooter. But, I very strongly recommend the Marlin. Don't let the initial start up issues with Remington scare you off. They are very well made and quite accurate to boot. I fully expect for mine to last the rest of my life and maybe even my great grand children will have as much fun with it as I have.