As always, comments are welcome, especially in this series if you disagree with a categorical choice of mine. I relish the challenge, and iron sharpens iron, right?
1.1 Paul, an apostle of Christ Jesus through the will of God . To those who are  holy and faithful in Christ Jesus, 2 grace and peace to you from God our Father and the Lord Jesus Christ.
3 Blessed be the God and Father of our Lord Jesus Christ, he who blessed  us with every spiritual blessing in the heavenly realms in Christ, 4 just as he chose us in him before the creation of the cosmos that we might be  holy and faultless in his presence in love, 5 he who chose us beforehand  in adoption through Jesus Christ in himself according to the purpose of his will , 6 in glorious  praise of his grace  which he bestowed freely on us in him who has been loved .
- τοῦ θεοῦ, Gen.: Subjective–θελήματος as a verbal head noun from θέλλω, where God is the enactor of the will.
- τοῖς οὖσιν, Ptc.: Substantival.
- Note: If the phrase ἐν Ἐφέσῳ is included, then I would alter the translation to: "To the saints and faithful who are in Ephesus".
- ὁ εὐλογητὸς, Ptc.: Subst.
- εἶναι, Inf.: Purpose (he chose us with the intention that we would be holy and faultless); Result (he chose us with the actual result that we became holy and faultless)
- προορίσας, Ptc.: Attributive (paralleled with ὁ εὐλογητὸς); Causal ('blessed be the God . . . who chose us . . . because he chose us'; less likely than Attributive)
- τοῦ θελήματος, Gen.: This one is quite difficult for me in several respects.
- If εὐδοκία is a verbal head noun (εὐδοκέω?), is it Objective (purpose drives the will) or Subjective (the will propels the purpose)?
- If εὐδοκία is not a verbal noun, it's between Attributive (willful purpose) and Attributed (purposed will).
All this to say, I have not come to a solid decision about how to classify this particular genitive.
- δόξης, Gen.: Attributive (praise of glory = glorious praise)
- τῆς χάριτος, Gen.: Objective (grace being the object of the possibly verbal head noun ἔπαινον)
- τῷ ἠγαπημένῳ, Ptc.: Substantival. There is bound to be a nicer way to translate this phrase, though.
Translated from UBS4 Reader's Edition (2007)