Great input from all. Effective shot-placement is assumed, and for this discussion I'm thinking chest-cavity.
Below are some general ballistics comparisons for the .22 range. LR and WM data from CCI website, Hornet and .223 from Shootingtimes. Drop based on zero at 200 yards. For the .22LR and 22WM both CCI and ShootingTimes give data only out to 100 yards, and no drop as are considered zeroed at 100 yards.
.......................................100 yards
..................300 yards
................................ft/sec
....ft/lb
...drop
......ft/sec
...ft/lb
...drop
.22LR 40gr....................897......72.....n/a*.......n/a*
.22LR 32gr...................1066......81
.22WM mini-mag 40gr....1319.....155....n/a*.......n/a*
.22WM v-max 30gr........1571.....164
.22H 35gr....................2278.....403...+3..........1135...100...-17
.22H 45gr....................2042.....417...+3.5.........947....90...-20
.223 40gr....................3120.....685...+1..........2297...469...-6
.223 55gr....................2747.....921...+1.6.......1905...443...-8
The 25-06 is not included as it is a much heavier bullet and I felt too much for the lower-end caliber choice.
Would a .22LR or .22WM be big enough for 'yotes? Out to what range? As the ballistics data sources only give data to 100 yards for these, I'd expect them to be a short-range choice only.
The Hornet falls in between to balance use between bushy-tails and 'yotes. But I do like the .223 for cost-and-choice of ammo over the Hornet, and the flatter trajectory.
Sure, the 30-06 could be used for 'yotes with a lighter grained bullet, but I'd think it would do too much damage if the goal was to save the hide. So for 'yotes and smaller I'm looking to the smaller-caliber gun of the two that would be owned, and the larger caliber for game bigger than 'yotes.
As long as you don't count small game in the CPX1 category, then I can bypass the .22LR, which in any quiz like this, I think that it's a given that you get a .22LR and it doesn't count against you.
Small game included... 22lr and 30-06.
Larger varmints and up... 223 or 243 and 30-06.
I'd go .22 long rifle and .308 win.
That .223 can be a bit messy on small game and now you can get more practice as well!
The .223
would be a bit much for rabbit-sized critters if one wanted to have something left for the table. Maybe the Hornet would be as well. OK, maybe we'll have to concede that owning a 22LR is a given...
The 30-06 has it's shortcomings for bear and bison, although a 220-grain would help. Therein lies the challenge in this discussion - there are tradeoffs when limited to two calibers. For it's all around versatility and ammo availability, I'd still stick with the '06 for the larger caliber choice. When hunting bear, just go with a friend that has the .338 or .375
If we concede the 22LR, then I'm still with the .223 and 30-06.