Purpose would be home defense, Mad Max with plinking as a hobby. Pretty sold on 5.56.
If you have children in the household, my advice would be to buy a Glock 9 mm pistol and that Hornady Rapid gun safe so that you could keep on your nightstand or kitchen countertop or whatever. With children around, you would need to keep a long gun in a proper safe and that is not an option in terms of self-defense.
If no kids, then the 5.56 is actually a pretty decent home defense option if you mount a light on the rail and could afford a legitimate CQB red dot like an EoTech or AimPoint. I would keep it on a wall mount in my bedroom or best central location, with a round chambered and the safety "on". Do
NOT use military ball ammo for self defense in a
rifle. At 3K fps you will be into your neighbor's house and the green tips/SS109 will not consistently yaw. Use a modern Law Enforcement / FBI protocol barrier blind loads like Hornady TAP or Nosler Bonded Defense. You can even find the 62gr Mk 318 SOST rounds in the Federal White Box - which are fucking bad ass and is the only widely distributed commercially available 5.56 military ammo worth a shit. For the most part ( outside the SOCOM community ), the commercially available LE loads are superior to the surplus military loads.
I personally have an AR in .308 which I keep in a safe, and a Glock 41 with a rail light on my nightstand or kitchen island and a Glock 30S with a Cross-Breed IWB holster for CC. The 41 has Hornady Critical Duty for defensive ammo and the 30S has Barnes TAC-XP. I keep my self defense mags marked with a silver Sharpie, because I reload and for legal reasons I want to have factory law enforcement ammo loaded for any personal defense situation if I can help it.
If no children around, and you trust your wife, then I say get the 5.56 with a light and Red Dot and have fun.
The pistol is easy to stow away and get around corners. But with both my arms extended in a combat grip the front sight of my Glock is likely about the same distance from me as the barrel end of my 16" AR shouldered.