An even earlier example of SOME of the elements popping up was the "Tales of the Legion of Super-Heroes" feature when it finally got its own series in Adventure Comics.

These early stories still had a lot of goofiness for sure (can you say Planetary Chance Machine?), but they had a lot of continuing plotlines. They had a member that got killed very early on only to revive a year or so later, then one part of a member who died permanently, then by 1967 a full member who died permanently. It had the developing of romances between members early on (Lightning Lad/Saturn Girl, Phantom Girl/Ultra Boy, Night Girl/Cosmic Boy, Star Boy/Dream Girl), and had members get kicked out, and one who betrayed them. Definite personalities were formed, with shy people (Violet), hot heads, a whole team with an inferiority complex (the Substitutes), an aggressive female leader (Saturn Girl), etc. It really came together when Jim Shooter starting writing it (at age 14!).