I'd vote .44 Mag for the OP's stated purposes. It's lighter, carries more rounds (than .30-30), great for short range deer-sized game, and can be loaded (typically down) for inside HD "better." The .30-30 in the short (16" "trapper") length can be a real unpleasant boomer and flasher/flamethrower. I also have .357 and it's great, but in the end the .44 is more versatile IMO. I don't use this type firearm to be a rangemeister with, so overall utility trumps most ammo cost considerations. IMHO, it's a popular misconception that .44 Mag--in popular/common loadings--has more felt recoil than the "typical" .30-30. They're different (.44 a comparatively sharper/shorter "cycle") but to me the .44 is a relative pussycat in the field, recoil charts notwithstanding (which is what folks like to quote but which measure force empirically, not felt. Neither is all that fun to shoot all afternoon with "full power" loads, but my nod still goes to the .44 in that department, especially if you factor in a shorter barrel. Weapon selection is crucial with the pistol calibers (particularly for .357). With my choice being Rossi (under a variety of importers over the years), then Marlin. The Win 94s were not designed for the short "pistol-length" cartridges, but seem to do "more ok" with the .44s than .357s, and of course best with .30-30. YMMV and I'm sure folks will chime in with their own good .357/94 reports. A poll of owners would indicate otherwise, if internet chatter is any indication. The 94 just doesn't seem to like the .357, comoared to other chamberings.
Take your pick between Win and Marlin on the .30-30...seems to be about a 50/50 world out there in terms of fans--with adherents on both sides having their own good points. I'm a lifelong Win fan with this cartride, but would not be averse to owning a nice older Marlin 336. Make mine the standard 20" carbine in either for the best compromise of capacity, handling and shooting.
Sum up - .44 16" trapper" in your brand of choice. I have both lengths and would take the 20" as my one and only, but the OP mentioned the shorter lengths for his focus and the trapper .44 is a handy little popper.