Vote as per the title.
Assumptions:
1) 5 player characters in the campaign.
2) The bulk of the game will be Tier 2-Tier 3.
3) Feats Yes, multiclassing No. (No dips!)
4) Assume you're trying to strike a balance between these goals:
a) Diversity in character concepts and builds.
b) Overall group effectiveness.
c) Shared class synergy (wizards sharing spells, druids being able to group wildshape, mass first round fighter action surge, etc.)
I'd say it was real close between Bard, Druid and Cleric.
Personally I picked Bard, because I think individual Bards have a bit more diversity and synergy than Clerics and Druids, but there's not a whole lot in it. Bards have more at-the-table build diversity than Clerics/Druids because they have Sorcerer-style casting, so each individual Bard is looking at different spells he can cast, much moreso than a Druid/Cleric.
My gut feeling is that healing magic isn't really necessary in a 5e game (with the possible exception of Healing Word), as Hit Dice can handle most of the out-of-combat healing. I also imagine a lot of people don't feel the same way, which impacts the rankings.
Healing doesn't factor into me suggesting Bard/Cleric/Druid, even though all three can heal. I agree that healing magic isn't vital.
However, spellcasting in 5E is extremely powerful, and these classes are well-rounded in ways that other casters and non-casters are not.
Unlike a lot of editions, everyone being the same class is likely to work pretty well with most classes. Fighters and Paladins are likely to be good, Barbarians okay.
Less well would probably be Rangers and Monks (and I'm not saying that just to be mean to Rangers/Monks), because there's a lot less synergy there, and a lot more "trying to do the exact same thing in slightly different ways". "Stop! I can only get so stunned!" to paraphrase Archer. And whereas all Rogues are likely to be strong at stealth and creating opportunities for each other, Rangers/Monks will be less so. They'll still work though.
All Warlocks would be fun but I think potentially very swingy and vulnerable to melee monsters. Even if one or more of them is a Hexblade, it's unlikely they can tank everything and still be useful when their most powerful attack is Eldritch Blast, a ranged attack, and thus given Disadvantage by an adjacent enemy character. Incantations and various spells can provide okay ACs (ish) and temp HP that would probably make them somewhat survivable.
Very least well would probably be Sorcerer/Wizard. Mostly poor ACs, and poor HP would mean that, even spamming cool leveled spells every encounter, you'd likely have budding Harry Potters bleeding out all over the place. All it takes is a few goblins winning initiative.
