All-purpose? Of the guns I have?
a 9mm handgun, with standard [13-17 round] capacity. Since carry was listed, probably a Browning Hi Power, as it would carry nicer than my full-sized Baby Eagle, which can hold 4 more rounds, due to the frame weight.
I like the idea of a Glock G17, as I can throw a .22lr conversion on it, but I just can't cozy up to Glock pistols. Nothing wrong with them. They just don't fit my hand right.
I also would be tempted to get a full-sized 1911 and run a .22lr conversion kit on it.
However, you mentioned one gun only and I am trying to avoid giving myself multiple calibers, as that seems to be cheating.
9mm is cheap for frequent range fun, it can be effective if I use the right round and aim well, and the ammo is EVERYWHERE [like .45acp?].
I can't get 100 rounds of any other major caliber for $20, but I can for the 9mm.
So I am leaning to Browning Hi Power.