Is there a definitive list of which episodes / scenes that they used for the classic doctors in The Day of The Doctor?
TL;DR: skip to the end for the complete answer, or read in order if you want to feel more involved in the search for the quotes.
Here's the transcript from Chakoteya of the relevant passage in Day of the Doctor:
DOCTOR 11: Oh, hundreds and hundreds.
DOCTOR 10: But don't worry, I started a very long time ago.
DOCTOR 1: Calling the War Council of Gallifrey. This is the Doctor.
DOCTOR: You might say I've been doing this all my lives.
DOCTOR 2 [on monitor]: Good luck.
DOCTOR 3 [on monitor]: Standing by.
DOCTOR 4 [on monitor]: Ready.
DOCTOR 8 [on monitor]: Commencing calculations.
DOCTOR 5 [on monitor]: Soon be there.
DOCTOR 7 [on monitor]: Across the boundaries that divide one universe from another.
DOCTOR 6 [on monitor]: Just got to lock on to his coordinates.
DOCTOR 9: And for my next trick.
So let's go through them in order, starting with the most recent.
DOCTOR: And for my next trick.
-- The Parting of the Ways (Series 1 Episode 13)
I can't find the line "Commencing calculations" in the transcript of either the 1996 movie or the 2013 minisode. Perhaps it comes from one of the audio adventures?
DOCTOR: Yes, sideways in time, across the boundaries that divide one universe from another.
-- Battlefield (Season 26 Serial 1)
DOCTOR: Almost there. Just got to lock on to his coordinates.
-- Attack of the Cybermen (Season 22 Serial 1)
DOCTOR 5: Soon be there.
-- The Five Doctors (Season 20 Serial 7)
These quotes are so short and generic that they're very hard to pinpoint simply by searching the transcripts.
The line "Calling the War Council of Gallifrey" was never said on-screen by the First Doctor.
Ah, I just found an article from BBC America which confirms the origins of all these quotes and clips:
The First Doctor’s face is from “The Daleks”—with the voice provided by mimic John Guilor—while the Second Doctor’s face comes from “The Tomb Of The Cybermen” and voice from “The Seeds of Death.” The Third Doctor’s face comes from “Colony In Space” and his voice from “The Three Doctors.” The Fourth Doctor’s face is from “Planet of Evil” and the Fifth’s is from “Frontios” while his voice from “The Five Doctors.” Both the Sixth Doctor’s face and voice come from “Attack of the Cybermen” and the Seventh’s come from “Battlefield,” while the Eighth’s face comes from the 1996 TV movie Doctor Who. Which just leaves the Ninth Doctor, whose face and voice came from “The Parting of the Ways.”
Here it is:
The archived footage shown during the Save Gallifrey scene for the different Doctors are as follows:
The First Doctor's footage is from The Daleks.
The Second Doctor's footage is from The Tomb of the Cybermen.
The Third Doctor's footage is from Colony in Space.
The Fourth Doctor's footage is from Image of the Fendahl.
The Fifth Doctor's footage is from Frontios.
The Sixth Doctor's footage is from Attack of the Cybermen.
The Eighth Doctor's footage is from Doctor Who (The Movie).
The footage from Colony in Space, Image of the Fendahl, and Battlefield have all been flipped to make it look like actual filming.
Source: The TARDIS Wikia