Assuming that the reason for the limitation was legislation, then for a long gun, I'd be mighty tempted to do what the Europeans tend to do; I'd probably get a drilling. Usually they are a SxS shotgun over a rifle barrel (12ga over 9.3x62 is one combo I've seen). Only real downside is slow reloading, and you're limited to iron sights so it's not the most ideal for an SHTF gun. But with that, one can hunt almost any game from quail to elk (depending on the rifle caliber). Considering that most game animals are taken at ranges under 100 yards the lack of optics probably wouldn't matter for most people. If ammo cost and availability were not an issue I'd love a custom 16ga over 6.5x55mm. However since those issues will probably dominate, 12ga over .30-06 (or .270Win) would probably be my choice.
If we found ourselves legally limited to only 2 guns, chances are handguns would have been eliminated from legal ownership along with EBRs. If that were the case, I'd probably choose a lever action carbine for my second gun. That would fill the home-defense/SHTF role reasonably, and would give another option for a hunting arm. I'd likely go for something like a .357 or .44mag, a .30-30, or possibly a Camp 45 or PC40 or similar if autoloaders aren't banned. Most likely I'd go for a .357mag lever action carbine as ammo is pleniful and cheap and a lever is almost as fast for aimed shots.
If it's for money reasons, I'd keep my Swedish Mauser and Ruger P944, and I'd sell the Turk Mauser and my wife's .38 revolver and my .22 (heresy to some I know, but that Swede just stole my heart). If it's 2 guns per person (rather than per household) my wife would keep the .38 and .22 rifle and only the Turk would go from the house.
But, even though money is tighter than I'd like right now, I'm currently working on increasing my gun collection, not reducing it. My priorities right now are to get a modern sporting rifle, then an EBR, then an HD shotgun. After that is taken care of, I'll be going after (in no particular order) a good CCW pistol for myself, another handgun for my wife, a lefty of ambi hunting rifle for my wife, more sporting rifles for myself (mostly bolt and falling block), a trap shooting shotgun, and numerous WWII era rifles.