The OP question was:
Do We Choose Him or Does he choose us?
The answer is: YES!
Jn 12:32 And I, if I be lifted up from the earth, will draw all men unto me.
(NOTE: Everyone at some point will receive an invitation from the Holy Spirit. Then it's up to us to accept or deny)
Genesis 24 is a shadow of our invitation: God, Abraham, Isaac, the Servant and Us
Genesis 24:
2 Abraham said unto his eldest servant of his house, that ruled over all that he had, Put, I pray thee, thy hand under my thigh:
3 And I will make thee swear by the LORD, the God of heaven, and the God of the earth, that thou shalt not take a wife unto my son of the daughters of the Canaanites, among whom I dwell:
9 And the servant put his hand under the thigh of Abraham his master, and sware to him concerning that matter.
(NOTE: Abraham sends his best servant on a sacred oath pledge (strangest oath, vs 2, I've ever read about, but I digress) On a mission to find Isaac a wife. To a land God revealed earlier to him earlier)
The servant meets Rebekah at a well:
15 And it came to pass, before he had done speaking, that, behold, Rebekah came out, who was born to Bethuel, son of Milcah, the wife of Nahor, Abraham's brother, with her pitcher upon her shoulder.
16 And the damsel was very fair to look upon, a virgin, neither had any man known her: and she went down to the well, and filled her pitcher, and came up.
57 And they said, We will call the damsel, and enquire at her mouth.
58 And they called Rebekah, and said unto her, Wilt thou go with this man? And she said, I will go.
(NOTE: Key point here - Rebekah has a choice - and agrees go & marry Isaac)
61 And Rebekah arose, and her damsels, and they rode upon the camels, and followed the man: and the servant took Rebekah, and went his way.
(NOTE: Abraham represents: God the Father, Isaac the Son of God, the servant represents God's Holy Spirit, Rebekah the bride represents the believer).
Jn 12:32 And I, if I be lifted up from the earth, will draw all men unto me.
(NOTE: Everyone at some point will receive an invitation from the Holy Spirit. Then it's up to us to accept or deny)
John 16:13 when he, the (Holy) Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
(NOTE: Abraham sent his servant to find Isaac's bride. God's Holy Spirit is sent to bring those WHO AGREE/the bride (Rev 21:9 & 22:17) to His Son the bridegroom (Matt 25:6 Jn 3:29)
(NOTE: Just like Rebekah, when the offer/call/invitation comes, we have the choice to accept or deny. My we all choose wisely.