I've had a 444 Marlin around 30 years ago. I wanted to shoot cast bullets in it. It worked fine. Never tried jacketed bullets. I am buying my second 45-70 lever rifle (Win and Marlin). Both the 444 and the 45-70 will put a big hole all the way through a deer.
So, IMHO, it comes down to ammo availability. If you don't reload, you should for either of these cartridges.
A 35 Remington will kill deer very well too. Although I have cast bullet molds for 35, I'd use 200 grain jacketed on deer.
A 358 Win would be more powerful - enough easily for bigger game. Again I'd use jacketed bullets.
There's many many others that would do very well too. A BLR in 308 would make a lot of sense if you don't reload.
