I had not really thought much about starting at level 0 before, but it sounds kind of interesting. How do you decide when to level up to 1st level? (Not looking for one 'right' answer, just wondering what each of you chose to do.) I guess it could even be just whenever the PCs themselves decide they are tired of getting their butts kicked and want to get on the road to being a badass.
Whoever survives the first adventure.
I'm going to be using this for my next campaign and here is how I am thinking of doing it.
I will schedule an 8-hour chunk of time for session-0, a level-0 game, lunch, and general hanging out together.
Session 0 will be maybe an hour or two. Everyone will be given a sheet of paper that is split into four sections. Each session will have a form for basic stats and equipment. All players will create four characters. Stats will be based on standard array. We usually roll, but this time I think standard array is quicker and helps people not get two attached to their characters at this time. Next everyone selects one background for each of their four characters and adjusts stats, proficiencies, skills, and equipment accordingly. That's it. Noboby is allows to write up any background for their characters at this time. That is done as part of the level 0 game.
Next, we vote on rule variants that will be used/allowed in this campaign (e.g., multiclassing, meat-grinder mode, flanking, longer rest times, healing kit dependency, alignment restrictions, class/race restrictions). DM has veto, but I generally just state anything I'm not willing to play. I also use this time to lay out some ground rules that are specific to this campaign. This will be a an old-school mega-dungeon crawl with a mega-plot involving the defeat of death cultists. Players will encounter real evil. I don't need to go too much into all this, because we've been playing together for years.
Next, I run a four-hour introductory adventure to the campaign setting. This next campaign will the be the 5e conversion of Rappan Atthuk, which was recently Kickstarted by Frog God Games. For example, for this adventure, I plan to have the party as members of a merchant's caravan travelling along the Sea Coast Road on their way to Felkor's Ferry. There will be a some small events to set the scene and one major encounter/event that will be the party-defining event to kick things off. It is up to the players to decide why each of their four characters are travelling to Felkor's Ferry and how the events share the motivations of the surviving character they choose to continue with.
After the adventure a surviving character is selected and a class selected for it. This will be a group exercise.
Going forward, as characters die, the player can replace their dead character with an adventurer who has come to Felkor's ferry (motivations up to player, so long as it make sense why s/he would join the party). The arriving adventurer must be one level below the lowest level surviving party member.