Obi-Wan Kenobi's journey, in order
To watch Obi-Wan Kenobi's story in order, start with Episode I – The Phantom Menace, then Episode II – Attack of the Clones and The Clone Wars. That's 6 out so far, about 15 hours, ending with Episode IV – A New Hope.
Obi-Wan trains Anakin, loses him to the dark side and watches over his son. Ewan McGregor and Alec Guinness share the role.
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Obi-Wan Kenobi's story in order

Episode I – The Phantom Menace
Obi-Wan is Qui-Gon Jinn's apprentice, and promises to train Anakin.

Episode II – Attack of the Clones
Obi-Wan uncovers a clone army.

The Clone Wars
Obi-Wan and Anakin as generals in the Clone Wars.

Episode III – Revenge of the Sith
Obi-Wan has to face Anakin.

Obi-Wan Kenobi
Ten years later, in hiding, he learns Vader is alive.

Episode IV – A New Hope
An old Ben Kenobi meets Luke.
Also worth watching

The Clone Wars: Season 1
Much more of Obi-Wan in the Clone Wars.

Episode V – The Empire Strikes Back
Obi-Wan's ghost guides Luke.
Questions
What order should I watch Obi-Wan Kenobi's story in?
Start with Episode I – The Phantom Menace, then Episode II – Attack of the Clones and The Clone Wars, and follow the list above: 6 in all, ending with Episode IV – A New Hope.
How long does it take to watch all of Obi-Wan Kenobi's story?
About 15 hours for the 6 out so far.
When should I watch the Obi-Wan Kenobi series?
After Revenge of the Sith and before A New Hope. It's set ten years after Episode III.
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