Why did Manwe choose the Vanyar as his favorite of the Elves?

Question

What unique quality does Manwe see in the Vanyar to make him love them the most of all Elvenkind.

Answer 1

We don't know

Very little was written about the Vanyar, so we're not told explicitly what qualities Manwë admired in them.

If I had to guess, I would suggest that they were the closest to the Elves of Arda Unmarred, the hypothetical result of a Music of the Ainur not disrupted by Melkor's discordance. We're told a few times in The Silmarillion that Manwë was the most attuned to the will of Ilúvatar; for instance:

Manwë was the brother of Melkor in the mind of Ilúvatar, and he was the chief instrument of the second theme that Ilúvatar had raised up against the discord of Melkor

^{The Silmarillion I Ainulindalë}

Manwë is dearest to Ilúvatar and understands most clearly his purposes

^{The Silmarillion II Valaquenta}

The Vanyar display a few qualities that would align with this worldview:

• They were members of the first tribe of the Eldar, all of whom accepted the summons to Aman; this is contrast to the other two tribes, who experienced discord in their ranks and divided into the Avari (who refused the Great Journey) and the Noldor and Teleri. As I pointed out in my answer to the above-linked question, the Vanyar even still identified themselves as this tribe:

  This name [Vanyar] was probably given to the First Clan by the Noldor. They accepted it, but continued to call themselves most often by their own numerical name Minyar (since the whole of this clan had joined the Eldar and reached Aman).

  ^{History of Middle-earth XI The War of the Jewels "Part 4. Quendi and Eldar" Part C: The Clan-names "Vanyar"}

• They were the greatest enemies of Melkor, wanting nothing whatsoever to do with him:

  Now in his heart Melkor most hated the Eldar, both because they were fair and joyful and because in them he saw the reason for the arising of the Valar, and his own downfall. Therefore all the more did he feign love for them and seek their friendship, and he offered them the service of his lore and labour in any great deed that they would do. The Vanyar indeed held him in suspicion, for they dwelt in the light of the Trees and were content;

  ^{The Silmarillion III Quenta Silmarillion Chapter 6: "Of Fëanor and the Unchaining of Melkor"}

Answer 2

Because they were being good boys and girls who readily accepted the summons to live in Valinor, didn't turn away on their way there, and didn't join the rebellion of the Noldor. They lived at the Valar's feet happily ever after and sang praises onto them.

All in all, they were the perfect idea of Elves.

Tolkien Gateway also states that Manwe and Varda loved the Vanyar especially for their great skill in poetry. http://tolkiengateway.net/wiki/Vanyar