I think the most practical solution is this:
1 - Big Game Cartridge. For me that's 7mm-08. Power enough to kill anything I intend to shoot within the ranges I intend to shoot without unnecessary recoil. One could also build an AR-10 around it for funsies. For you, the big game cartridge might be anything between a 300WM and a 6CM. Pick your poison.
2 - Shotgun. 12 gauge for me, but arguments can be made for 20. Allows you to shoot turkeys on the ground, birds on the wing, rabbits, clays. Add a slug barrel or a separate slug gun, and you've got a medium to large game cartridge for closer shots, dense woods, and dangerous game. Legal in straight wall areas. Also works for home defense.
3. 9mm. As described in the OP. Innumerable options for pistols and carbines.
4. 22 lr - pistols, pumps, levers, carbines, bolts, ARs. You can get anything in 22 and shoot it cheap. Also the perfect solution for small game and some birds.
The practical solution, however, lacks pizazz, and I would have to change something to make it more fun:
- ditch the 9mm. I don't really care for pistols anyway. Replace it with a fun and capable small and fast cartridge like 223, 25CM, or your 6ARC. Now you've got a varmit rifle that can also harvest medium game that's easy to shoot for fun and accuracy. Of course some of these also have the the AR option.
You, however, don't hunt birds and don't seem to have any interest in shotguns, so your list looks different. If I were to comment specifically on your list, I'd say this:
- forget the 7PRC. It's more gun than you need for almost anything, so it's going to be relegated to the back of the safe while you take the fun stuff out to the range and woods. Replace it with a 6.5 PRC so you've still got something big enough for all of NA and much of Africa that's also tame enough for the teens (especially suppressed).
- ditch the 6.5CM cuz you no longer have a gap to fill between your ARC and your PRC. Make that 4th cartridge whatever you want for fun, since your bases are already well covered. For me, it's a lever gun. Research shows that lever guns are undeniably the bestest guns. . . . I'm sure there's a pie chart somewhere that proves the point. A Marlin 336 in 30-30 for the whitetail woods? A Henry 45-70 as your sidekick in bear country? Maybe the new S&W 1854 in 44 mag for straight wall states? Any of those would be a blast, and I would find any gun safe incomplete if it lacks the fun of a lever action rifle.
-Keep the 6ARC and the 9mm. Love what you did there.
