I just started the MQ last night with a character.
My character doesn't have a smartphone, so there is no uesp available. Spoilers burn her soul.... Trying to make a decision from in-game information... is difficult.
The Blades...
1. Can I join them?
2. More importantly though... What is their philosophy? Do they want to see all the dragons destroyed? Or just the evil ones that want to destroy us all? But the Blades, according to Delphine (in my mind, my voice says "Jensine") also support the Dragonborn, to protect her or him.
Now the Dragonborn, I would assume, good or bad morally, would have something invested in the non-destruction of his teachers.... If you agree to follow the way of the Voice, and learn and study, it seems that the Blades would be enemies, or really, really bad neighbors, to the Greybeards, and to those who want to study the voice rather than use it for destruction.
So if the Dragonborn joins the Blades... doesn't that fight itself?