He doesn't mean that Bran is a great story teller. Tyrion means that Bran's journey of hardship from broken boy to seer was the most convincing one of all the possible candidates. He was the rightful Lord of Winterfell as Ned Stark's eldest surviving son, and yet he never sought that position.  You'll recognize that Bran's story was that of the Last Hero from Old Nan's tales. His was always going to be a story for all the ages. That makes a great story because it will be so long remembered. It's something people can get behind. This guy pieces together the pieces we do know pretty convincingly, and he does so without having to guess about things we don't know like the Children's real tale. When you look at what Bran actually did this season, he's the prime mover on setting up the complex domino that brought him to the exact spot he ended up in. He's the one who insisted that Sam tell Jon of Jon's true heritage at the exact moment needed. So Jon told Dany, who started to fear he'd claim his birthright, and that's why Bran got Jon to tell Arya and Sansa, who told Tyrion, who told Varys, who was so convinced he got himself executed immediately after telling Tyrion that he hoped he was wrong. And Bran intervened to save Jaime, in a curious sense: he didn't tell anyone else that Jaime had crippled him. That way Jaime wasn't summarily executed, and would survive to try to return to Cersei only to be captured by Dany so that Tyrion would free his brother to die in their sister's arms at Dany's hand and be found that way by Dany's Hand, which made Tyrion resign in disgust as Hand after accusing Dany of murdering a city, and get thrown in the dungeon for treason, where Jon would visit him and be implored to save his sisters. And earlier Bran had told Tyrion Bran's own story. Then once Jon and Tyrion were both in the dungeon, Tyrion had a lot of time to think. None of the other Lords Paramount were anything at all. And the whole council was completely dominated by Winterfell and Winterfell's family and supporters: Uncle Edmure for the Riverlands, Cousin Robin with Lord Royce from Vale, Cousin Gendry for the Stormlands, Sam for the Reach, etc etc etc. None of them was himself a candidate for the kingship, but he would certainly support Ned Stark's only surviving son in that position. That made Bran an easy pick. And not just by the council sitting that day. By Bloodraven. He had already chosen the next king by the end of the first episode of the first season. We just didn't know it yet.