Note that this is subtly different from the “one level in every class” thing; this is about taking your levels one at a time, starting from level 1, rather than a fully-finished level 13 concept.
Could this be at all viable? What order would you go with?
I’ll give an honest try.
Your build will rely heavily on magic items and a cooperative DM. That’s 1 uncommon at level 1, a rare at level 5, and a very rare at level 11.
Custom lineage 13/13/8/13/13/14(+2) Feat: Resilient Wisdom (the only feat you’ll get so it should be this)
Magic item: Cloak of Elvenkind (for hiding)
Sorcerer, Aberrant mind - Gets CON/CHA saves. Con is good for when people hand you scrolls to concentrate on and CHA is the only thing you’re good at. Has mind sliver (to support your allies’ actually useful spells) and dissonant wispers to chase things away. Can telepathically talk. Also take shield, silvery barbs, and chromatic orb. Stay away from the front, hide, and pray.
Rogue - expertise in stealth and perception. At least you can be a scout with your hiding and telepathy.
Cleric, order - heavy armor and you can let your stronger allies attack more with voice of authority. Also grab healing word.
Bard - more caster progression and some d8’s to help your friends. Tasha’s hideous laughter might do well long term.
Warlock, hexblade - in case you really need to hit something with a rapier, now you can use CHA
Magic item: Amulet of Health (suddenly you can be a frontline distraction!)
At this point things aren’t too bad. You can scout or shield/rapier with 20 AC, +1d6 sneak, upcast dissonant whispers/chromatic orb, and support your friends a little with silvery barbs/d8s/mind sliver. Sadly, out side of more slots and some hp you start getting nothing from here on out.
Wizard - full caster, get utility spells
Druid - full caster, utility
Artificer - half caster
Ranger - half caster
Paladin - half caster
Barbarian - d12 hp
Magic item: +3 amulet of of the devout (gives +3 to all spell DC’s and spell attacks)
Fighter - d10 hp
Monk - yey