[Tuor of Gondolin]

To jump in with another quote from UT about selecting Bilbo:

'How would you select any one Hobbit for such a purpose?' said Gandalf. 'I had not time to sort them all out; but I knew the Shire very well by that time, although when I met Thorin I had been away for more than twenty years on less pleasant business. So naturally thinking about the Hobbits that I knew, i said to myself: "I want a dash of the Took" (but not too much, Master Peregrin) "and I want a good foundation of the stolider sort, a Baggins perhaps." That pointed at once to Bilbo. And I had known him once very well, almost up to his coming of age, better than he knew me. I liked him then. And now I found out that he was "unattached"- to jump on again, for of course I did not know all this until I went back to the Shire. I learned that he had never married. I thought that odd, though I guessed why it was; and the reason that I guessed was not the one that most of the Hobbits gave me; that he had early been left very well off and his own master. No, I guessed that he wanted to remain "unattached" foe some reason deep down which he did not understand himself- or would not acknowledge, for it alarmed him. He wanted, all the same, to be free to go when the chance came, or he had made up his courage. I remembered how he used to pester me with questions when he was a youngster about the Hobbits that had occasionally "gone off," as they said in the Shire. There were at least two of his uncles on the Took side that had done so."