Expert Long Rester
Just go with something close to what their original 1e write-ups were. I'd probably go with level 3, as by that time everyone has their subclass.
Tanis: Fighter (battlemaster) NG. Half-elf. Outlander background
Tasslehoff: Rogue (thief) N Halfling (lightfoot). Far Traveler background (kender wanderlust)
Caramon: Fighter (champion) LG human. Mercenary veteran (SCAG) background
Raistlin: Wizard (enchantment) N (NE leanings) human. Cloistered scholar (SCAG) background
Goldmoon: Bard/Cleric (life) LG human. Noble background
Riverwind: Ranger (hunter) LG human. Outlander background
Sturm: Fighter (knight) LG human. Knight of the Order (SCAG) background
Flint Fireforge: Fighter (champion) NG hill dwarf. Guild Artisan background
Tika: Fighter/Rogue NG human. Folk hero background (not the best fit, but nothing else comes close to "tavern wench")
Gilthanas: Fighter (eldritch knight) (or wizard bladesinger) CG High elf. Noble background
Laurana: Fighter (banneret) CG High elf. Noble background
As for the more specialized class features and feats, I'll leave those out for now.
I like this.
As they progress I could see Raistlin taking some levels in Undying Patron Warlock, Pact of the Tome.