Well... I have a 45 BC carbine reamed to .454. I reload for it because factory ammo is expensive and puny. Good for anything I'll hunt under 100yds. Also good for primitive seasons if you need that, so my choice because you can load it easy mild or hot, and I think the nicest looking Handi. Not made anymore so not readily available.
My 45-70 is great. Very expensive store bought ammo, and way more than 'my' wife could handle. Loaded mild it's not much more powerful than a hot .454. Won't work for pistol caliber hunt season.
I have 2 30-30 and am looking for more. Not primitive, but it's good for anything else. Ammo is 1/3 price of 45-70 or .454, half .45 LC... cheaper than anything but .223. You can buy it anywhere. Easy to reload, mild or hot, especially in a Handi. More bullet variety. Best walk around rifle I think. Supposed to be one of the most accurate Handis, still manufactured, and notice they command top resale prices on the classifieds.
So I vote for the 45 BC carbine and reloading asap, or the 30-30 and make do for awhile with store bought ammo. Anything else is too much, too expensive to shoot, not primitive, not common or whatever.
Note that my 3 favorites are all rimmed cartridges on SB2 frames.
JMHO. Be well...