Go read this. THAT is the way to start a campaign!!
Don't like science-fantasy? Who cares? Take that general mold and fit it into the style of campaign that you want to run.
You want to run a modern-day rpg? Have the characters wake up in an overturned SUV, injured all to hell, not remembering who they are or how they got there. Have several ambulances arrive to treat them OR have another identical SUV arrive with people in it offering to help them if they move quickly. (Are the people in the SUV friends, foes, or something else?)
You want to run a superheroes rpg? Have the characters wake up scattered in the destroyed remains of your campaign's version of the 'Hall of Justice'. They don't remember what their powers are; they don't remember anything about themselves. (Are they all good guys or are some of them villains? Who did this? Why?)
You want to run a standard fantasy rpg? Have the characters wake up in a room, each in a bed, with no memories and with various physical injuries. A man enters the room who seems suspicious. He tells them that he found them in the (woods, ravine, dungeon corridor, etc) lying amidst a dead group of (pick your monster--but perhaps he doesn't tell them) and that he brought them back to his abode. (All sorts of good question possibilities.)
You want to run a straight sci-fi rpg? Frankly, very little to do differently.
You could follow steps 1-3 of that article exactly. The rest will have to be altered as necessary to match your theme, but you need to use the attribute checks, some major combat encounter, and the clues that point to 'another one'. Who is that other one and what is the connection to the player's party? Those questions may never be answered or they might be the point of it all. But THE POINT of all of this is that the players will start this campaign feeling the way that we all did the first time that we played an rpg.
This was probably the best blog post that I've read in the past week, and I just had to write something to complement it.
Although I have to be completely honest: Tonight has been a most fruitful blog reading evening. Two other posts that I have to highlight are this one and this one. The first talks a little about the megadungeon in your campaign; the second talks about something that most people who run wilderness campaigns probably never think of. Both posts are excellent! Hopefully, when I have time, I'll write a little something to go with each of those as well.