I could definitely recommend some particular storylines!
The Sleeper Awakens (Tales of Suspense #72-74, Cap #101, #148) – Captain America fights a bunch of the Red Skull’s giant Kirby robots. They are awesome Kirby robots.
The Cosmic Cube (Cap #115-119) – the Red Skull gains the powers of God, Cap fights him and wins, thanks to Cap’s determination and the power of love.
MODOK! (Tales of Suspense #94, Cap #119, 124, 132, 133) – Kirby’s giant Olmec baby head assassin is hilarious and surprisingly socially conscious, if still evil.
Cap vs. Nixon (Cap #166-176) – Captain America is targeted by the Committee to Re-Elect the President, foils the Secret Empire’s attempt to overthrow the U.S government, unmasks Nixon as the head of the Secret Empire, Nixon commits suicide rather than be arrested. Cap resigns and goes in search of America.
Madbomb! (Cap #193-200) – Captain America and the Falcon team up to save America from a bomb that will turn all of America into mad rioters, a conspiracy to restore monarchy to America, an underground murderball league, Captain America travels through time, and Arnim Zola tries to transplant Hitler’s brain into Captain America. One of the best Kirby runs ever, therefore one of the best comics runs ever.