In Eastern Orthodoxy, is it most important for the efficacy of the sacraments that they be administered canonically by an ordained priest (who is in apostolic succession), or the fact that God is the one who works in and through the Holy Mysteries? Or is it both (or something else)? A discussion of canonical decisions made during the Novation and Donatist controversies would be helpful, as well as the decisions of Church councils. I am specifically interested in the sacraments of Baptism and Holy Communion (the Mystical Supper).
I'm not Orthodox and I don't know much on Orthodox theology, but I'll try to answer from what I have found.
AFAIK Orthodox Church shares the ex opere operato doctrine though the understanding is not the same (here near the bottom). This means that the answer is "God". The action of the priest is necessary, but not so much, it's less important than in Catholic understanding.
The priest is necessary for Eucharist (like in Catholic Church). For baptism the priest is not necessary: under extraordinary conditions, even a layman can baptise.