On deer size game out of carbines I found that in a .44 Magnum any of the expanding jacketed soft points between 240-250 grains work well. (I save heavy bullets or hard cast lead for game animals larger/heavier then deer!) Out of a .357 Magnum carbine I look for Jacketed soft points between 158-180 grains. Any of these used within their range/energy limitations should work well. (.357 Magnum 50 - 75 yards on deer size game. .44 Magnum 125 - 150 yards on deer size game.) Within these parameters these two cartridges have worked well for me. (Handguns need to have the range adjusted to reflect the user's capabilitiy.)

Good luck!

P.S. If you find that the .357 Magnum is not quite as effective as you'd like....it should be a simple chamber reaming job to open it up to .357 Maximum, (by any gunsmith with a little skill). The side benefit is that you should still be able to shoot regular .357 Magnums/.38 Specials through the same firearm. (Though because of the freebore it might be a little less accurate in the .357 Magnum. Sometimes it is....sometimes it isn't.) I'm not entirely positive the conversion is possible with the Rossi SS, but I believe it is. The .357 Maximum out of a carbine increases muzzle velocity by several hundred feet per second over the standard Magnum. And muzzle energy proportionately.