So, which comes first, the union to or acceptance of Christ as Lord? The easiest answer to this question is to say that they are simultaneous, and I am not sure that one's beliefs as regards Calvinism vs. Arminianism matters in liking that response. The problem is that then one might wonder how something can cause something that is at the same time as it. That problem does not occur for transcendent acts, as they are all everywhen, but this seems a very immanent act, one of the most immanent, God with us, acts. Thus, I would like to explain it immanently.
Before addressing the direction of causality, it is necessary to show that there may be a causal direction without time in between the events. This is relatively simple if one thinks about it right. I release the ball, it falls. There is no time in between my release and the ball's fall. The moment I am no longer holding the ball up, gravity draws the ball down. I pick up the ball, it rises. I am picking up the ball in order to raise it, and my picking up the ball is the cause of its rising, yet they are simultaneous.
Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?” And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.” --Acts 2:37-39
First, it is implied here that our repenting and being baptized are what we we do in order that we might be saved. it even seems to be implied that receiving the gift of the Holy Spirit is directly linked with that salvation. We might even say that our repentance causes us to receive the gift of the Holy Spirit, and (by him) salvation. So much for unconditional election? Not quite. "For the promise is for you and your children and for all who are far off, everyone whom the Lord our God calls to himself" Anyone who repents will be saved, and many are called, though few chosen. But this does not mean that there is no other work which causes us to obey and repent and be baptized in the name of Jesus Christ for the forgiveness of sins. "So those who received his word were baptized, and there were added that day about three thousand souls." (Acts 2:41) Those who received his words. How do we receive the word of God? If we receive it, we will obey it, and if we obey, and repent and be baptized, then we will be saved, but our ears are stopped up.
Then how do we hear? It is by grace, but what grace? We receive the Holy Spirit after we repent, and we receive the word before, can we receive the word without the Spirit? Jesus tells the Twelve, well before he even died, "To you has been given the secret of the kingdom of God, but for those outside everything is in parables, so that 'they may indeed see but not perceive, and may indeed hear but not understand, lest they should turn and be forgiven.'" This is the difference, some have been given the secret of the kingdom of God, others cannot understand it. What is this giving? It is God's grace which allows us to be saved, allows us to repent. In some sense it may be what occurs in his ordaining some to salvation that he places this secret in us. What is given? The secret of the kingdom of God. The Gospel truly heard, not by human words or human ears, but by the spirit God tells us the Gospel. Then we can, and will, repent and be baptized for the forgiveness of sins.
So what is the order? First God ordains, then he speaks to certain people, even through ridiculously incompetent humans, then those he spoke to hear, for, when God acts in order that a thing be heard at some time by someone, they cannot miss it (they might hear it at a later time than they think they ought to have, but perhaps God chose to keep it from them for a time), and because they hear rightly they repent and are saved.
Thus, in preaching, teaching, evangelizing, we speak the Gospel. Some will hear but not understand, others will appear to understand, but not finally, still others will persevere to the end. Our job is merely to say words and deeds that they may hear if they have ears, if God speaks through us. It is like a man in a foreign country telling people that there is a danger. He does not know who will understand him, yet he tells them all in every way he can think to. The fact that some know his language already, and some will not understand however hard he tries, is unimportant. Our job is to speak in order that those who hear might respond with repentance, and we can do this boldly since those who will not hear have either not been given ears to hear, or it is not yet their time. At the same time, we cannot be proud that we have brought some number to Christ, since it was only because God gave them the ears to hear that they heard, we are only the tool. When it seems that what we say has no effect, we ought not be discouraged. Our job is to tell the good news, not to make people hear it, though we desire that they would.