First, let's review the Biblical meaning of righteousness. The first paragraph of the Righteousness article of Baker's Evangelical Dictionary of Biblical Theology edited by Walter A. Elwell (1996), shows how faith in Jesus leads to the Trinitarian God producing righteousness in us, which comes in stages (emphasis mine):
God the Father is righteous (just); Jesus Christ his Son is the Righteous (Just) One; the Father through the Son and in the Spirit gives the gift of righteousness (justice) to repentant sinners for salvation; such believing sinners are declared righteous (just) by the Father through the Son, are made righteous (just) by the Holy Spirit working in them, and will be wholly righteous (just) in the age to come. They are and will be righteous because they are in a covenant relation with the living God, who is the God of all grace and mercy and who will bring to completion what he has begun in them by declaring them righteous for Christ's sake.
Then, in the theology of the Reformers, it's helpful to distinguish between two (or even three) kinds of righteousness:
- Righteousness of believers coram deo ("in the presence of God") a.k.a passive righteousness, the righteousness of God imputed to us, that is the basis of our salvation. This is what NigelJ's answer describes.
- Righteousness of believers coram mundo ("in the eyes of the world") a.k.a. active righteousness, which cannot merit salvation. This is imperfect righteousness as we walk in the Spirit, trying to obey the New Testament commandments. These works are pleasing to God because they are the fruits of the Spirit. The prerequisite is the 1st kind.
- "Righteousness" of unbelievers as they try to obey the voice of their conscience. These are not pleasing to God and also cannot merit salvation. Faith in Christ is necessary for this kind of righteousness to be turned into the 2nd kind.
Why is God selecting the faithful instead of the righteous for salvation?
The simple answer is that God still requires us to be righteous to enter heaven (Matt 5:20) , but knowing that we cannot be righteous on our own He sends Jesus as the way for us to become righteous. Jesus's work on the cross is the fulfillment of God's promise to provide this way, which is called the plan of salvation.
How do we apply Jesus's work of salvation to our lives? It's through faith in Jesus, which then unlocks God's gift of new spiritual life (which is called being born again). Armed with the new spiritual life, in which we are united with Christ, Christ (the Holy Spirit) helps us obey commandments so we can live righteously, although until the Holy Spirit finishes His work in us (called sanctification), we will still commit sins when we fall into temptation.
How does free will come into the picture? Before we have this new life, our will was not completely free, but in bondage to selfishness. After being born again, we need to use our free will to reject the old-self way of living and to embrace the new spiritual way of living, which is called walking in the Spirit, Gal 5:16. In our new life the Holy Spirit gives us grace that assists our free will to choose the spiritual way. Being faithful should result in desiring to be righteous (Blessed are those who hunger and thirst for righteousness).
CONCLUSION: Saying that God requires us to be faithful rather than righteous will lead to misunderstanding. As we can see in the preceding section, faith and righteousness are intimately connected. God requires righteousness from us, but because humans abuse their free will resulting in the condition of the Fall, we can no longer live righteously on our own. It is no wonder then, that in this corrupted condition God requires us to have faith in Jesus as the ONLY way God provided for us so we can live righteously.
In other words, people who believe they can be righteous on their own are lying / delusional. That is why God selects the faithful who hungers for righteousness and who out of desperation begs and trusts Jesus to provide the way. We are like sheep who need to follow Jesus as He leads us to heaven through trials to refine us (1 Pet 1:6-7).
I hope this explanation resolves your confusion. I purposely answered in general terms that I think most mainstream denominations can agree. Different denominations have
- different teaching on how this righteousness is applied to us: imputed, imparted, or infused.
- different teaching on how this faith should be expressed. Some require the sacrament of baptism.
- different teaching on the sanctification process. Some require the sacrament of Eucharist and Confession.
But all denominations teach that by the time we enter heaven we will be fully sanctified, a condition that will fully reverse our current Fall condition. In that glorified condition (with a new body, no less) we will then be able to obey God's commandments perfectly in heaven (i.e. being righteous) with pleasure and ease.
Why God made a world where faith was necessary?
This is your follow up question (edit 3). The Bible didn't really answer the question because the Fall already happened very early in the Bible (in Genesis chapter 3) and the theme of the whole Bible itself is this plan of salvation announced as early as Gen 3:15 (Protoevangelium) to which faith in God's unfailing love and faithfulness (OT) and in Jesus (NT) is the necessary response.
The book of Job acutely demonstrates how even God refused to answer Job's question of why the righteous (like himself) suffers and the wicked prospers, pointing out that a human being is asked to have faith (trust) in God who is great beyond measure, who is His own category that cannot be compared to any creature. God merely assured Job that He is greater than the most awesome evil creatures (God's Sovereignty Over Leviathan and Behemoth). Still, a human's desire for explanation cannot be quenched, which is okay as long as it doesn't caricature God the way Job's friends did. How then, to reconcile God's character, God's omnipotence & omniscience, the goods we experience in creation, and the presence of evil?
The usual answer (example: C.S. Lewis's Problem of Pain summarized here) is that this world may be the only possible arena where:
- all rational creatures (human and angels) have a meaningful free will, EITHER to love God and other creatures OR to disobey their God-given conscience
- to create an environment for free will to be expressed, the laws of nature need to have some stability (a sword doesn't turn soft when used to kill) which can cause pain and great evil such as wars and genocide to happen, forcing humans to face the REAL CONSEQUENCES of their acts of evil as well as the REAL GREATNESS of their acts of charity
- the drama of Fall and Redemption takes place in the full presence of God: from Adam's sin in Eden to God's incarnating Himself in Jesus to the Holy Spirit's activities today, to impart healing and grace to those who have freely chosen to make God #1 instead of putting themselves above God; in other words: God is not aloof up there but gets down to the most heartbreaking place offering love, strength, and hope
Faith, then, can be seen as human response to God's tainted creation, in contrast to despair (culture of death) or materialism. Together with the community of the faithful, we embrace God's original vision for creating this world: for humans to partake in the world's goodness while avoiding evil by choosing responsibly aided by grace. The Great Commission asks us, as the body of Christ (salt and light of the world), to bring this vision to the unsaved, so they too will be invited to join the Kingdom of God and enjoy the goodness of God's original creation. It's faith in God's rescue mission to prepare the world for the future fulfillment of God's promise of the new heaven and earth.