I had always seen Tanis as a Ranger type, what with the hunting leathers and being a woodsy type. But in 1e Rangers had spells that would complicate matters (though they didn't get them until a higher level than later editions). I could see him as a fighter, maybe battle master with more leadership type maneuvers, and the archery feats with an outlander background.
Cameron could be a champion fighter with a folk hero or mercenary background, but later on he becomes a gladiator and general, so battle master might be more appropriate.
Riverwind as a hunter Ranger with the Tribe Member or Outlander background seems fine. Gooldmoon as a life cleric & noble background, with restricted access to spells (via the Blue Crystal Staff). Tas as Rogue with far wander background seems good. Flint would be a fighter champion with an Artisan background might be the best fit.
I would put Strum as a Samurai or Cavalier with the Knight of the Order background. I would lean more towards Samurai, as Strum doesn't do a whole lot of cavalry work. Tika could be a Rogue, maybe a fighter with the Folk hero background.