Even though I own a 870 I really like my mates 11 87, that same mate also owns a 10/22, but I much prefer my 597.
I almost put a CZ 452 instead of the 597, but the fun factor of plinking with the semi just nudged it forward.
I refuse to even fathom such a horrible world where I'm relegated to only 2 guns. since this is the rifle forum I suppose you are only talking about long guns, in which case my 3 handguns are still safe from confiscation so I guess I would pick my Savage No 4 MK1* and a Seekins precision AR15.
For two long guns, I'd pick pump actions, a Mossberg shotgun and a Remington, in an all around useful rifle caliber.
Pumps will generally work with anything, and, with a little practice, are fast to operate.
Two rifles? 30-06 and 22lr. I could hunt any mammal in North America + defend myself.
Two guns? 12 guage pump (18-20" barrel) and Browning Hi Power. Could hunt with the 12 guage if necessary and self defense.