I am a firm believer that every family should have as a minimum the following:
A centerfire rifle
A repeating Shotgun
A service style handgun
A .22 rimfire.
These four firearms will allow any family to survive darn near anything.
The makes and models are open to suggestion but a good example and inexpensive would be...A Winchester 30-30, Mossberg 500, Smith & Wesson model 10 and a Ruger 10-22.
For the rifle you can go a variety of ways such as the AK or SKS options, Expensive AR15 or Ruger Mini-14, Less expensive surplus Enfield or Yugo Mauser. The Shotgun and pistol is also open to a variety of choices. The key is to get them.
If it were me and I was in a bind financially I would go for the shotgun first and then the handgun to be followed up by the rifle and .22.
I see the shotgun as being the first choice to defend the family and houshold after a catastrophe. I survived 3 hurricanes last year and had the shotgun at hand in the house. An excellent show of force and easily recognizable to riff-raff. In my case I also had a GLOCK 26 in the pocket as backup and a "always" armed gun. A KelTec Sub 2000 in 9mm with GLOCK 30 round magazines was also available. I did not get the rifle until this spring and I went with a Colt LE Carbine.
This setup with a Ruger 10-22 rifle and Ruger .22/45 pistol covers any eventuality. I have some extra handguns for competition and concealed carry but they are bonus material.
If I were looking to recommend a system for new shooters I would go for the Mossberg 500 in 20 gauge to start. A S&W Model 10 with a 3 inch barrel to have available if you needed to be armed quietly and a Winchester Model 94 for the rifle. A .22 rifle of most any variety would be last.
I think only one gun is a false economy for emergency use. The need for the significant other to be armed if you must cover the front and rear of the house should not be overlooked. Especially in the event you had the one gun break or get confiscated. A second gun "put up" would not leave you unarmed. Even a lowly .22 Marlin rifle from Wal-Mart would be potent medicine for most looters.
If only one...Shotgun, one each per spouse.