I would recommend at least watching the original Godfather. What a brilliant film!
I am generally not a fan of 3-hour epics - for me an extreme length often suggests an over-indulgent director, who does not care for his audience, has been working with a weak-willed producer and a poor editor - but The Godfather is so tightly written that it becomes fast-paced and genuinely entertaining in every scene.
Brando is mesmerising in his limited-screen-time titular role - the studious efforts of his transformation into Don Corleone are written all over the pain, fatigue and jadedness of his face (and hidden behind deliberately clumsy make up). A well deserved Oscar.
Much more underrated, but equally good, is James Caan as the eldest “Test Child” who has grown up to be entirely spoilt and petulant, always threatening to go off-the-rails, and does not wish to understand the Mafia etiquette. His presumed birthright as the next Godfather leads to an arrogant and unsubtle nature that is tragically (and perfectly) captured.
You don’t necessarily have to follow up with the sequels. From the opening couple of teaser shots to the gently terrifying final scene, The Godfather tells a beautiful and circular story.
