Barbarian is the best class for a supporting character without a subclass.
- Most hit points (1d12 hit die).
- Unarmored defence (Start lvl 1 with 18 AC, 16 Dex[+3], 16 Con[+3] and a shield[+2].
- Extra attack at level 5
- Fast movement (10 foot speed increase at level 5).
- Rage - you still get this classes defining feature at level 1 without a subclass.
Compare Ranger, faring much worse without it’s subclass/archetypes; Barring hunter’s colossus slayer or beast master’s animal companion and you have arguably lost Ranger’s most essential features.
Hot take: The most important aspect of a supporting character is their staying alive. Because the most annoying would be having to constantly revive a nerfed PC. So Wizards are out, rangers and warlocks and sorcerers are out, your left with cleric, paladin, fighter, druid.
Well fighters are okay with second wind and action surge but its a debatable second fiddle to Barbarian hit die and fast movement.
Losing a druidic circle is harsh but workable. Cleric is fine but boring, party healer if your into that. Paladin flavour-wise could be a headache keeping their oath etc.Barbarian won’t die, is easy to RP and doesn’t-really lose anything of import when compared to other classes.
To make the decision even easier, consider that if your secondary character is a spell-caster, you will spend time choosing spells and considering things like area effects and concentration. Some people enjoy this aspect of the game and would then be wise to pick a Druid, Cleric or Paladin. By contrast the Barbarian is low maintenance and could still pick up a cure wounds spell and spare the dying cantrip with the magic initiate feat.
Subjective support: I have played D&D, read PHB.