I am not a stickler for a particular method of rolling up characters, as long as everybody at the table agrees on what that method is. Personally, I like seeing where the dice rolls take me, but I appreciate the fact that my particular proclivities are far from universal.
Once everybody agrees and people start rolling dice, I begin to illicit information about each character at the table, with two critical goals:
1. Figure out how the various characters know each other prior to game play. I hate wasting time on role-playing this. It always makes more sense to hash out these details at character creation because some characters are just never realistically going to meet at a tavern to go adventuring together. Plus, the given stories about these relationships can have a much deeper effect on the campaign than the whole tavern scenario. Finally, it allows the campaign to hit the ground running. Instead of wasting time trying to justify adventuring together, the players just go on an adventure together.
This can be done in a number of ways. The simplest is just ask the players how their characters know each other and suggest some possibilities if they seem stumped. In my most recent campaign, I created a random table which players can roll on to see how their character knows one other character in the party. Everybody has to choose someone different so that all these relationships intertwine.
2. Figure out what relationships the characters have to various NPCs in the campaign world. For example, clerics can be at the beck and call of a bishop and magic-users can belong to the Mage Guild. This accomplishes a couple of things for me: it grounds each character within the world and it provides a source of information to the players about the world itself with the benefit of possible patronage. The cleric from above could have a specific task that they need to accomplish for the bishop and the magic-user could be delivering a scroll to the local representative of the Guild.
The First Adventure
Once these two things have been established for each character, I provide rumors and possible missions to each player through the various relationships that their characters have. I then allow the players to decide what rumors they want to investigate or what missions they want to undertake.
Note: it is very important that these rumors all tie in to adventure locations I am prepared to run. Usually, it is pretty easy to weight the choices in favor of the adventure location I am most interested in, but I never dissuade players who deviate from that particular plan. If I am not prepared to follow up on a rumor or mission, I don’t offer that choice.
What all of this does is place agency squarely in the hands of the players. If the whole character creation process has gone according to plan, every player has a character that has a background tying them to both the other characters at the table and to people and organizations that exist in the campaign world. Then these relationships inform the choices the players make as to which adventure they want to go on in their first session together.
In the end, all of these things invest the player in the campaign world. They have goals, not just for themselves, but for the various people and organization around them. The game becomes more than just the characters, it becomes a world that they have the power to shape through their own choices and actions.