I guess I'd think about light weight, and relatively low recoil for that light weight. (Why bother with heavy stuff if you don't need it?) So, .243, .257 Roberts, 7x57, 7mm08, .300 Savage, .30-30, .308...
Seems to me a bright but low-powered scope is important.
Absent blind luck (which will beat brains or skill, anyday), there ain't no such animal as a bullet which will penetrate brush or tree limbs without deflection.
I dunno; some 30 or 40 years back, the folks at the Rifleman did some testing. They took several rifles, from around the .257 Roberts on up to a .45-70. They shot through a clump of brush, which from the pictures looked like no more than finger to thumb thickness of branches; the clump might have been some ten feet through.
The targets varied in distance behind the clump. It didn't matter about pointy-nosed bullets or round-nosed bullets. It didn't matter about .25 stuff or El Bigboy. What mattered was the clear span between the clump and the target. Anything over ten yards or so was almost always a miss.
Everything deflected to some degree or another.
FWIW, Art