This is an old storyline that has taken on many facets, from books, television shows and movies. We all have our favorite doomsday scenario. The amount of research on the subject is vast. Whichever scenario you choose make sure the players feel uncertain about everything. I believe that this is key in running an Armageddon campaign. The adventures should continue through a campaign. There is so much that can happen to characters during the aftermath of Armageddon. If the players know that there is a campaign ahead the uncertainty levels also rise.
One of the best places to start the campaign is immediately after the sentinel event. Decide what causes the end of civilization as we know it. The cause can be a pandemic, EMP, prehistoric weather change, caldera explosions, meteor impact, world financial crisis, nuclear attack, biological or fantastic events. Some of you may come up with other causes that will fit your campaign. In either case you can tell if the players would buy in the cause. This will add to the validity if the players can believe that this can happen.
Another thing to consider is gear and encumbrance. This campaign will have to place some importance on both of these. Supplies will become scarce and extremely valuable. Also the ability to carry such things becomes more difficult as health wanes. The difference in carry 40 pounds of gear and 10 pounds of gear becomes more than evident walking across the desert. As the GM you should plan for some sort of system for your players, especially if you normally overlook encumbrance and gear choices.
If you decide to run this type of campaign you can really add uncertainty by not revealing to the players what is going to happen. You can have the players make characters of the present time and work in the same area. They can have different occupations. Almost every business in the world will have many people working different jobs. Each person is almost certainly diverse in their personal life as well. A couple of examples would be the female HR representative at a silicon manufacturing company is a lifelong NRA member with a stash of guns in her trunk. The male custodian may be a discharged Army combat engineer. The character possibilities are endless. At the beginning of the campaign the characters will all come together because of the event and by sharing a common thread; the work with each other. All character skills and knowledge become important.
The end of the world has begun. What are you going to do?