The Erie order of morning and evening prayers are not really traditional, but a hybrid attempt to provide something practical and useful.
The traditional Old Rite prayer rule, if canons are used, is to use canons to the Saviour, the Mother of God and the Guardian Angel.
Opening prayers - Come, let us worship - Psalm 50 - creed - canons - It is Truly meet - Trisagion through to the Lord's prayer - troparia - Lord, have mercy x40 - prayers of the canons (omitted if the rule is read congregationally)- More honourable - dismissal.
The Hodigitria canon is used on Tuesday night and the Annunciation canon on Saturday night. On other days it's the canons in the book: Sweet Jesus, Thanksgiving, Guardian Angel (Greater Canon on Sunday night)
However, this doesn't stop you from using other canons, though you could chant a menaion canon using the order of the molieben, of course.