When you're Catholic, you generally go to the Catholic church closest to your home. It might not be a perfect church in every sense, and you might go to other Catholic churches in your area when it's convenient, but there isn't often a difficult process involved in choosing a church.
For a Protestant things are very different. Now, there are some people who will say, "Christian is Christian," and pick either the closest church, the church with the most inspiring speaker, the church with the comfiest seats, or the church with the best music. I have to say right out that this is wrong. There are very different things taught in different churches, but since illustrating that sounds like another topic to me, let's assume for now that I'm right: Different things are taught in different churches. You will get a different set of "do's" and a different set of "don't do's." You will be taught different things about who Jesus is, and different things about what he wants from us. You will be presented with different parts of the grace that God offers.
The point is that it matters what a church teaches, and not just how it teaches. If two churches teach equal amounts of truth, go ahead and choose one based on location or music style. Accordingly, from this point, when I say "church," I will generally mean either an independent non-denominational church or an entire collection of churches (or denomination) with a single authoritative body.
So the real problem is, how do I pick a church that teaches the right thing? Of course prayer plays a part, but prayer doesn't happen in a vacuum. We have internal and external influences of all kinds. Thus, I've known many people who have prayerfully considered which church to attend, yet they all ended up in churches that were quite different in their beliefs, from "non-denominational" (which I think of as micro-denominational), to Wesleyan denominational, to liberal Episcopalian, to Seventh Day Adventist.
To illustrate the crux of the problem: Someone I know changed churches because he felt his Pastor had been telling him he had to vote Republican. Just as easily, someone might leave a church for telling them to tithe 10%, or to avoid homosexual acts, or to give up wine and dancing. Some of these people might be right in disagreeing with their Pastor, and others might be wrong. The thing is that ultimately, the Pastor has no authority, and the individual church-goer has all authority. You see, every Pastor is voted into place by either a literal vote of the congregation or by a vote of attendance.
If we think about this it ultimately means that each person is a denomination unto themselves, and must serve as Biblical scholar, arbiter of conflicts, guardian of sacred tradition, etc.
Let's see how this matches up with the Bible. In Acts 15 we can see the Council of Jerusalem, where a binding decision is made by the Church leaders, and it is promulgated throughout the Church. This only works in an authoritative unified Church.
What happens if I looked around and finally found Last Church of Mesa, where everything seemed right, but then all of a sudden the Pastor tells us the church leaders have made a decision? Now we are no longer allowed to drink beer! I know the Bible doesn't tell me I can't have a cold one while enjoying my televised sports program, so I go across the street to Hip Fellows' Fellowship, where I'm pleased to find out about the Beer and Televised Sports Ministry.
Similarly, let's remember what Matthew 18 tells us that Jesus said regarding church discipline. First the individual confronts the one in need of correction, then a small group, and if he still hasn't listened he is brought before the church. If he will not heed the church, he is to be shunned (or excommunicated). Once again, this only works in an authoritative unified Church.
So, what happens when I go back to the Last Church of Mesa (because they do have softer seats), and I start receiving negative remarks regarding my Beer & Sports t-shirt. If I get wind of them even thinking of bringing me before the church, I'll be back in the hard (yet hip) folding chairs at Hip Fellows' before they can even blink.
If we recognize this reality, it means that churches become clubs of like-minded people, and not places where we can go to really have our minds changed, and bring our hearts more in line with the ways of God.
This is why it is in fact impossible to choose a church. If we choose a church we are granting the church authority, and what we have given, we can take away, so the choice is by its nature impermanent. Also, we have no ground, no authority from which to really grant a church authority in the first place. And if we assume we do have authority to go so far as to choose a church, we have indeed become a church unto ourselves.
If we cannot choose a church, a church must be chosen for us. Who has authority to give us a church? Only God. Our choice would then be whether to accept what God has offered us. It must be a Church from God not from men. Certainly it will contain a lot of crazy people, but nonetheless, it did spring from a seed planted by Christ, and its roots still draw upon that source.
What would such a God-given Church look like? As I pointed out above, it should be unified and authoritative. Besides this, it must have history that can be traced to the time of Christ if it is the Church of the Apostles in Acts 15. It should show at least a little semblance of the temple-centered Jewish culture it separated from in the time of the Apostles. It would hopefully still have a strong presence in the Mediterranean, where the Apostles first spread the faith. It would probably be widely available around the world, so we could find it if we looked.
Now it would just be the icing on the cake if it were the largest unified Christian body in the world, if it had figurehead who personified its unity, if it were centered in a city mentioned in the Bible (and it would be ironic if this city was the seat of the fallen empire which once executed our Lord), if it had a Christian hall of fame and centuries of theological work to draw upon for guidance and inspiration, if it were responsible for the original evangelization of most of the Christian world, if it had decided upon the books of the Bible, and if it had painstakingly hand-copied the Scriptures for 1500 years before the printing press (and before all the little denominations which claim the Bible as their base).
If we recognized something incredible like this had happened, what right would we have to choose a church? We could only come to the conclusion that God had given us all a big shiny obvious Church as a gift, and all we could do is accept it.
