I have Handi Rifles in 22 Hornet, 30-30, 357, and 45-70. Plus a 45-70 Buffalo Classic. My hunting is about like yours. My pick if I could only have one would be the 30-30. I do like the 45-70 though. You will appreciate a rimmed cartridge in a break barrel. Most 45-70 factory loads will be loaded to trapdoor pressure levels unless you go to one of the boutique cartridge makers. That’s ok though, they are plenty for hunting and your shoulder will thank you. Recoil can be brutal in the light Single shots.
One difference between you and I is that I do reload. I second the opinion that you should buy a Lee Classic Loader, or better yet, the Lee hand press and a set of dies. The single shot will handle spritzers and it is no mean feat to load the 150 grain bullet, I like the Hornady Spire Point, to 2500 feet per second. Hodgdon Leverevolution is a good powder, H335 is almost as good, just 100 feet per second or so slower. Reloader 7 will push a 110 grain bullet to 2700-2800 FPS, makes a good varmint load. And the Hornady 170 grain flat point makes the 30-30 a dandy pig rifle with Leverevolution powder pushing that bullet along at 2300 FPS. I do imagine it would be a good bear round as well.
The Henry 45-70 interests me, when they came out with the 30-30 and 357 I got real happy, if they come out with a 22 Hornet life will be complete. I will have one of each by the end of 2019. 357 is here but I have not shot it yet. Really need that 22 Hornet Henry!