Only Three? Dang, thats a toughie, I'd have to give it a tie for the pistol and rifle between two, the shotgun is a easy choice for me.
Pistol: Either a 1911 Government model in .45 or a Smith model 19 with a 4 inch barrel. The 1911 for ease of finding ammo and mags, ultra reliable , and has fairly quick reloads also the slim profile of the single stack system means it can be concealed relatively easily . The smith for the simple fact that I'm a hunter and there is virtually no handgun caliber (one can make the case for the .44 spl/mag and the .45 colt) that can beat the versatility of the .357 mag and for its weight class the model 19/66 are the best ones hands down to carry, A 4 inch tube will allow easy concealment (unless your one of those lightweight pansies) and still make full use of the magnum option, .38s are also very common.
Rifle: Tie between the M1A Springfield and Marlin 1895 in .45-70 government. Yep, I know thats two very different firearms but here me out. The M1A would be a much better "battle rifle" and in is chambering of .308 winchester we run the added benefit of shooting 7.62 NATO, it can hunt further than that lever action could, ammo is relatively cheap for it considering even the russian and serbian makers make ammo in this caliber. Magazines are going to be easy to find new or surplus M14 ones, and the system it uses is very reliable in virtually any climate. Ok so how can I top all those good things with a "old school" lever action that isnt the best shooter past 200 yards? Several answers come to mind but the best one no one thinks about involves casting and reloading. I can cast my own bullets and hunt easily anything in the world with the proper loadings, ammo is plentiful but expensive in most of your big box stores, the lever action takes away the "nuisance" of carrying around more weight on magazines but you trade off a much smaller ammo supply at least that you can carry.
Shotgun: Easiest choice ever! The Mossberg 12 guage pick whatever config. you want (88,500,535,590). The 870 is completely acceptable to but my main issue with that one is if something breaks in the ejection system, the mossberg is very much a parts drop in system while the 870 if ever needing work on that issue, one either needs to send back to the factory or employ the services of a skilled gunsmith, both of which may not be an option under the circumstances you listed.
What are your choices followed by a brief explanation why. Remember, this is all about compromises with the goal of maximum versatility in a doomsday scenario since no one in their right mind would ever limit themselves to one of each.
