I kinda used a combination... the characters were created fairly much independantly and didn't meet for a while.
The first was a priest who, belonging to an organised religion, was sent on a mission to deliver an important message in a distant land. So off he goes, fights some undead on the way, then lets a whole tribe of goblins sneak up on him. He surrendered and wasn't heard of again for a while.
The second was a peasant who was working with a scythe when his farm was attacked by a certain tribe of goblins. After the community saw the raiders off, he went after them for vengeance. He found the priest tied up in the back of the dungeon; despite hating each other's guts, they had to work together to survive on the way out.
And because I only had two players, that was that for the first adventure. But I introduced a couple of extra characters in the second adventure under DM control (they later shifted to player control, becoming PCs). Strangely, the NPCs were the most reluctant to go adventuring...
Oh, and the previous paragraph is the only part not yet chronicled in my webcomic (linked below). So I won't give details. It's quite fun, though. Let's just say that finding someone else's hand in your pocket can have unexpected consequences for all parties involved.
The origins of the first two characters were player-generated, by the way. Their intersection was my idea.