As luck would have it....
I was in the middle of reading this thread when I had to visit the "reading room", and as luck would have it, I found an old article that has some information that may still be valid. In April 1988 Guns & Ammo publisheed an article about pistol caliber carbines, which included the following information.
In .357 Mag, the Marling 1894 they tested delivered the following:
125gr Winchester JHP 2,183fps MV
125gr Remington JHP 2,113fps MV
145gr Winchester Silvertip 1,841fps MV
158gr Winchester JHP 1,738fps MV
They got 3-4inch 100 yard groups with the 125gr loads
They got 2-3 inch 100 yard groups with both the 145gr and the 158gr loads.
Groups were shot with open sights.
Now, I realize this info is 20 years old, but I don't see either the rifle or the ammo getting any worse in the last 20 years. Probably a bit better. The author, Mike Venturino, considered it accurate enough for deer at 100 yards.
Current ammo intended for "bigger" game hunting should increase the performance of the carbine in the game fields. Most 125gr loads are intended as defensive handgun rounds, and may not perform well on deer size game, considering their light jacket construction, and the increased velocity from the carbine barrel. The now popular 180gr bullets should do well, HOWEVER, the Marlin is not tolerant of rounds that are too long. If you want to shoot the 180gr loads, check their length carefully, to ensure that they will feed through the action. Many years ago I watched a gentleman who had loaded some 210gr LRN bullets in .38 Spl cases jam a Marlin solid. Even in the short .38 cases, he had loaded the very long 210gr RN to a length that would not feed from the tube magazine, tying up the gun, and requiring the rifle to be disassembled in order to clear the jam.
Factory loads should be ok, even the heavy 180gr, but you would be wise to check carefully before stuffing them in to magazine tube. Over long rounds can be singfle loaded, and will work fine, butg trying to feed them from the mag is asking for a jam.
The 1894 Marlin is a fine little carbine, I have one, an older gun (no crossbolt safety) bought last spring, used, but looking like new for $300.
Practice a bit, so you learn how the rifle shoots, and get used to the drop between 50 and 100 yards. Load it with bullets built for the game you intend to take (and this will include hardcast SWC for some game), do your part and the rifle and ammo will do theirs adequately out to 100yards for deer size critters. One nice thing about the Marlin is that, if it doesn't go against your sense of esthetics, they can be easily scoped. A low power scope or a red dot sight can be a useful aid for shooting at longer ranges, especially if you are like me, getting to the point where the iron sights aren't as sharp and clear as they were 20+ years ago.