Looking for justifications you all use to have your player characters group up- do you simply start a campaign with group already or do you play out a meeting? Campaigns I have been involved with have started:

Individuals meet for first time at funeral for mutual friend

Group wake up as prisoners 

Childhood friends 

Future ideas involve any kind of social gathering  (e.g. a wedding someone wants to stop from happening)

House of Elrond style emmissary to meeting 

Do you require your group to factor in a communal element as part of their character creation or do you let them go wild and fix after? 

I will usually have my PCs have in-game relationships with one another ala Fiasco type relationships. Sometimes, they are tailored more for the campaign, depending on things. 

In the future... I may make more guided reasons the party is together, for example, they are all newbie members of a guild/faction/military/etc. 

I always tend to get that 1 player who wants their character to go off on their own adventure, so I try to get them to understand that that isn't gonna be possible and to make their character be someone who wants to stick with the group.

With all the prep my current group did, the one thing they DIDN'T do was come up with a reason to come together. I just gave them an open mission that they all came together for. Since then, i've been finding ways to prod them to get motivation other than "advanterang". So far, the only thing built by them is two of the characters are unknowing half-siblings, and being a druid and ranger they are feeling the bond between them. Otherwise, the players are slowly coming to me to work out a legit motivation for glomming together as individuals.

one time, my players were all responding to an ad calling for mercs

I like the add for mercenaries- if I inform my group that they reply to the add and have them generate part of their backstory that would motivate them to join sellswords that probably has lots of storytelling options

Have one of the PCs be given the "mission/job" and be responsible for hiring others to join on the adventure. They can RP the interviews of each of the other PCs as they join.

In one campaign I ran, the party had agreed to have already formed a mercenary type group before we started. It was simple, but it made my job SO much easier, because each PC knew from the start that they'd be sticking together, and nothing was shoehorned in. There were still intergroup friendships, rivalries, etc but everybody was constantly working together. It was one of the smoothest games I've run, to be honest.

I've had this discussion a few times with my son (also a DM) and we did come up with one possible solution. As we use milestone advancement, the assumption can be made that the party members did some adventuring prior to reaching level 1 and it was, during this period, that they decided to team up. Precise details can then be elaborated upon as the campaign progresses. 

I had one campaign where I didn't have an integrated party at all. All Characters had clear cut goals, and their own "adventure hook" which pulled them into the narrative - but none of them knew each other at all, and none of them started in the same location. Of course - purely coincidentally - all their goals happened to be connected into a single set of events, and by the end of the first session, all the Characters were  in the same scene. I don't know if I'd do that much DM tap-dancing again, as involved shifting the spotlight back and forth in a 6-way Party split - but it was a fun experiment.