1) My favorites tend to shift with new discoveries of songs, like hopping from one like to another. Right now, my current favorites are Toeto - Megurine Luka, Outer Science - Ia, Masked b***H - Megpoid Gumi, and Sweet Devil - Hatsune Miku
2) Some of the best, to me, is a bit of a hard thing to pin point exactly, so it's really up to you what the best are.
3) What I see it as, there are five essential songs that almost EVERYONE knows. They're:
World is Mine - Hatsune Miku
Just Be Friends - Megurine Luka
Matryoshka - Hatsune Miku and Megpoid Gumi
Love is War - Hatsune Miku
Ievan Polkka - Hatsune Miku

A good place to find some more songs is -> http://plug.dj/plug-dj-vocaloid-hangout/
The website is called Plug.Dj, and it's basically a place where "djs" play whatever they want. In this case, it's Vocaloid.
If you create an account, you can add songs that are played that you like into a playlist.