Mine likes a lot of stuff. The microgroove barrel of the 1894C can shoot lead well if the pressure curve is right to match the bullet hardness. Too low on the pressure and accuracy will suffer as well as cause leading. Getting the right powder and load combo to do this is sometimes tricky.
For plinking loads I like a hardcast 158gr RNFP or LSWC from a local supplier (Proofmark Bullets in Burgess, VA). They are really hard and bevel based and I had some trouble getting them to shoot accurately. Finally, I hit on a load of 7.0gr WSF for a pleasant shooting load that is accurate (for comparison, 5.5gr of WSF with a 158gr LSWC is a 38 Special +P load). The RNFPs make a better plinking load in that they are more accurate in my gun; they are more flat based than beveled.
Another favorite bullet is the Lyman 358156CG. Driven by 15.0 gr of 2400 and a CCI 550, these are proving to be very accurate at 100yds and pleasant to shoot. I think this might be a good hunting load.
I also had good luck with the Rem 140JHP with a full load of WW296. The Rem 140 seems to get along well with the 1894C. Velocity is outside of the bullet's design envelope so I wouldn't necessarily recommend it on large game, but other designs of similar weight might be impressive.
Finally, the Rem 158JHP or a Hornady 160 JTC-SIL driven with a published max load of Lil'Gun was giving me around 1910fps and excellent accuracy. If you plink something with that load, it's PLUNK .