Keven posted in his blog about which 4 guns, if you could only have 4, would you pick.
Go read his blog, good for his stats, then come back.
http://www.exurbanleague.com/misfires/2016/06/06/four-guns/There are two assumptions here. This is strictly a political limitation, not an apocalyptic, or EOTWAWKI. Secondly, that "gun" is as ATF currently defines it, is what's limited to 4. Barrels, grips and other parts are still freely available.
The Sig 320 is an excellent tool kit for caliber and size versatility. One frame and half a dozen calibers and 3 sizes. Again assuming multiple barrels don't count toward the 4 limit.
A shotgun, naturally. 12 gauge of course and again one that can take multiple barrel lengths so that it can be used for multiple sports and game. You pick your favorite model here.
NOW here's where Kevin and I differ. AR-10 or AR-15. Pick one, only one. With the 10 you have all the .308 spin offs. 6mm, 6.5mm, 7mm, 7.62mm, and 8mm. With the AR-15 you get a weaker set of cartridges. A variety, but probably not as many "factory" rounds. Again, are you choosing for hunting purpose, 3-gun, NRA competition, or zombies? PICK JUST ONE because:
I think the fourth gun should be a .22lr semi. Yes you could get an .22lr upper for the AR-15, but it's a kluge. A good .22lr will let you hunt smaller varmints, plink and enter some competitions. My preference is the Varmint barreled Ruger 10/22. Threaded, just in case though.