Really depends on how you define "story". Hashirama may have had the biggest effect on the Naruto universe as a whole, and Minato probably had the most influence on the character that Naruto IS, but as for the story that is told in Naruto, Itachi's decisions and character probably played the most decisive role. However, he also has had way more screen time than the other two, so I'm not sure it's even an interesting discussion.
I'd say Itachi under normal circumstances but since his secret probably won't be a public knowledge, only those who know of it would be influenced. So yeah, Hashirama hits the spot since he's the first to introduce us the will of fire and all that.
Hashirama had becouse evrithing is somehow conected to his actions in some way
Senju Hashirama!"the greatest ninja of his time and the only man i had ever admired."-madara.
They all have equal importance.
Hashirama made the shinobi world what it is by creating Konoha. He then saved Konoha by defeating Madara in battle.
Minato made various jutsu and banged Kushina to give us our hero. He also saved Konoha from Madara.
Itachi saved Konoha from the Uchiha clan, and kept Madara and Danzou in check for years. Also responsible for indirectly keeping Naruto safe and making Sasuke the way he is.
At the end of the day, if not for any of them the Narutoverse would be fucked in half.
To be honest, the man with most influence in the Narutoverse has to be Tobi if he really is Madara: he's responsible for forming Konoha as much as Hashirama, he's the one who caused the events to make Naruto the way he is now, his actions lead to the destruction of the Uchiha clan and the corruption of Sasuke.
He also created akatsuki, manipulated an entire country and is now waging war against the world.
I see Minato as the main protagonist of the background.
Now that we have gone through a large part of the war, and have seen more, what are people's opinion.
i vote minato, he laid the foundation for naruto to grow in power and he stopped the kyuubi from destroying the village
honestly the story of naruto flat out cannot be told without minato
Yondaime, hell even without the whole kyuubi accident he still fathered the world saviour, the messiah, the-boy-who-lived Naruto.
You can't get more influential than that
Still Hashirama. Without him, we may not have gotten Konoha and quite possibly no Minato or Naruto. If he killed Madara at that time, Kushina would probably still be the jinchuuriki. Kyuubi made Naruto into what he is. Hashirama basically established the first hidden village, and the war between him and Madara, Senju and Uchiha, is what set off teh current events: Uchiha Massacre, Tobi freeing the Kyuubi, etc.
I think Madara's the most influential, not counting Rikudou Sennin and his sons. The effect of Madara was felt even before he was ET'd.
He saved Konoha before he died,and after he died.
He save Naruto during the war... so Naruto could be the hero of the war.
He is in the process of changing Kabuto and Sasuke.
Without him, there wouldn't be a Konoha.
Itachi probably wouldn't have had to kill his clan, as they probably wouldn't have plotted a coup.
Itachi wouldn't think the way he did, and would not act in the same way.
Therefore he wouldn't have had the chance to save Konoha at all.
Sasuke also wouldn't be a missing nin if Itachi hadn't killed the Uchiha.