In Adventure Comics 323 (6/25/1964) Brainy is nearly killed accidentally by Spider Girl, turns downmultiple chances at succeeding Saturn Girl as Legion Leader due to fairness and is made fun of by Jimmy Olsen (Elastic Lad)

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Did you know the green in the Superman side of Composite Superman was from absorbing Brainy's powers? This was revealed in Worlds Finest 142 (4/30/1964) Also note Robin seems to know Brainy but they have never met on page.

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In Adventure Comics 319 (2/27/1964) Brainy is the first to be selcted by the notoriusly sadistic "Planetary Chance Machine"

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In Adventure Comics 310 (5/29/1963) Brainy once again works closely with Saturn Girl to defeat a descendant of Mr. Mxyzptlk. Brainy working with Imra as the 2nd smartest Legionnaire will continue as a theme for decades.

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"Now to shine Brainiac 5's Ray on the Infinite Monster" ~Supergirl
If you read last year's Action Comics 1026 you may remember the same shring ray solved a very similar problem ;-)

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"I'm no villain although my ancestor was! I'd gladly sacrifice my life to save your, any time!" ~Brainy
"Nobly sacrificing yourself might impress the girls of the 31st century, but it still gets you killed, no matter what year it is" ~Kara

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"Please... Please... Don't hate me...!" ~Brainy
Af first Kara is suspicious of Brainy as he explains his relationship with his ancestor further. Remember she was just hanging out with the citizens of Kandor in the previous story.

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"I am Brainiac 5, Supergirl... The great-great-great-great-grandson of the space villian who was Superman's foulest foe!" ~Brainy
Remember at this time the Original Brainiac was an alien.
He would not be revealed as a robot until Superman 167 (12/19/1963)

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"A handsome, green-skinned youth approaches the club table..."
The editor's narration reinforces Kurt Swan's dreamy pencils in the first frame where we see Brainy's handsome green-skinned face.

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