As an addendum, I just wanted to make a note about the redemptive meaning of suffering, its role in justice, and how Christ fulfilled justice for humanity through His own suffering.
It can be quite difficult to understand how suffering of any kind can be efficacious when we think about it as an evil. In order to understand how it can be, though, one simply has to see that it isn’t the suffering itself that is efficacious, but our interaction with it.
Human suffering is the natural consequence of sin. This is revealed to us in Genesis. Other religious and philosophical backgrounds approach the question of suffering differently, saying it’s an indivisible part of life, or that it’s a result of the gods/God acting upon us, or that the physical world is itself evil, etc. Genesis gets away from all of that and reveals to us that human suffering is the consequence, or effect, of sin, which is disobedience to God.
As it is a consequence of sin, it is therefore a component of the justice of sin. There are two things that happen when we sin. Firstly, we offend God, and damage our relationship to Him. Secondly, we hurt ourselves, and cause damage to our very nature. This is so because our nature is created by God, and is therefore like Him in its own limited way, and when we sin we act in a way that is contrary to God, which implies that we act contrarily to our own natures. So, the sin has this two-fold effect, we offend God by acting contrary to Him (and necessarily His will), and we damage ourselves because in sin we act contrary to our nature.
Justice is a matter of equity. When we commit a crime, we’ve offended or deprived another person. Justice is the matter of restoring that deprivation, or healing the offence (actually both). In the matter of humanity’s sins against God, true justice must both heal our relationship to Him, and restore what has been lost, or damaged in ourselves (our natures).
A further principle of justice is that the punishment, or restitution, must be appropriate to the crime committed. That is to say, if money was stolen, money or its equivalent must be returned. If injury is caused, injury must be repaid in kind (this usually comes in the form of jail time: the injury has somehow deprived the offended party of some form of freedom, such as freedom of mobility, freedom to earn wages, etc, thus jail time is sentenced to deprive the offender of his freedom). This is important, because the punishment for our sins against God must include both the nature of the offence as well as the consequences of the offence. And the nature of the offence of our sins is disobedience and the consequences are suffering and death.
To enact proper restitution for our sins against God, then, we must endure suffering and be obedient. Christ accomplished this completely, so redemption (the healing of our relationship to God) is accomplished, and salvation (the restoration of our natures to perfection) is possible.
But how does His obedience and sacrifice (acceptance of the consequences of sin: suffering and death) affect healing and restoration in us? The offence against God was satisfied by Christ’s obedience and sacrifice, thus we are redeemed because the satisfaction that was demanded by God was against the human family, not merely against Adam. For if it were, we could not have been affected by Adam’s sin. As for salvation, that comes about through the mysterious union that He allows us to have with Him. As members of the Church, we are members of His Body. We are one flesh with Him. So, we share in His obedience and sacrifice when we are both obedient and sacrificial. Ours and His become one and the same act, not two separate acts. Thus, the salvation wrought by Christ is extended to all men who unite themselves to Him, because through Him, their obedience and sacrifice are His, brought to perfection.
Also, for another aspect of this question, please watch the following presentation on the Trinity. You don’t have to watch the whole thing if you don’t want to, but starting around minute-mark 42:00, the presenter makes the case that the doctrines of redemption and salvation depend of the Trinitarian nature of God. You will see how this ties to the question of justice, as I’ve discussed above. Enjoy! 
youtube.com/watch?v=Rsfmbbpe2pA
