The 2nd century system of salvation

There were three doctrines that I would call fundamental to second and third century Christianity's system of salvation:
1. A works-based final judgment
2. Christ as a teacher of goodness and righteousness
3. Free will

In this period the Christian belief in free will is regularly vigorously defended by writers. It is contrasted to the Greco-Roman concept of Fate (predestination), and also to the gnostic idea of Natures (unchangeable inner natures). The strength of these endorsements of the freedom of the will seem to largely derive from the universal belief that humans would be judged by God in according to their character and deeds. Several writers comment that the fact of God's judgment of us implies that it is within our own power to meet that judgment else we cannot be held accountable. (This is known in moral philosophy as as the "ought implies can" argument, generally attributed to Kant).

This also is clearly defined in the teaching of the Church, that every rational soul is possessed of free-will and volition; that it has a struggle to maintain with the devil and his angels, and opposing influences, because they strive to burden it with sins; but if we live rightly and wisely, we should endeavour to shake ourselves free of a burden of that kind. From which it follows, also, that we understand ourselves not to be subject to necessity, so as to be compelled by all means, even against our will, to do either good or evil. For if we are our own masters, some influences perhaps may impel us to sin, and others help us to salvation; we are not forced, however, by any necessity either to act rightly or wrongly, which those persons think is the case who say that the courses and movements of the stars are the cause of human actions, not only of those which take place beyond the influence of the freedom of the will, but also of those which are placed within our own power. (Origen 230AD, First Principles, Preface 5)

The concept of Christ as a teacher of goodness, monotheism, morality, and righteous living who brings man to the knowledge of virtue and the knowledge of God is easily the strongest view of Christ's atoning work in this period. This conception of Christ as a teacher is universally present and in virtually every writer is the dominant model. Even in the theology of Irenaeus (fairly unique in this period for his Recapitulation (theosis) model of the atonement), the conception of Christ as Teacher is very much present in his writings and is co-dominant with Recapitulation. Emphasis is made at various points by the writers of this period on how Christ is the greatest teacher - the validity of other moral teachers is not diminished by this in their opinion, since all true moral teachers are considered inspired by the spirit that was in Christ. Clement of Alexandria in his work The Teacher (Paedagogus) attempts to demonstrate Christ's superiority to all other moral teachers through showing how he utilized every single form and type of rhetoric and moral exhortation known to Greek Rhetoricians. Origen expresses it with a nice image:

Suppose some one ignorant and uneducated to become conscious of his defects, either through the admonition of his teacher, or simply of himself, and then to put himself in the hands of a man whom he thinks capable of leading him into education and virtue; when he thus surrenders himself, his instructor promises to take away the lack of education and to give him an education; not, however, as though the educating and the escape from the want of it in no way depend on the pupil having offered himself for treatment: he only promises to benefit his pupil because he desires to improve. Thus the Divine Word promises to take away the wickedness, which it calls the stony heart, of those who come to it, not if they are unwilling, but if they submit themselves to the Physician of the sick (Origen 230AD, First Principles, Book 3, Chapter 1.15)

The concept of a final judgment by works is universally presupposed during this period. It is stated as Christian doctrine by the Apologists in their presentation of Christianity to outsiders. It appears explicitly or implicitly in almost every work of this period. The fact of and belief in a final judgment according to deeds is consistently utilized for moral exhortation and to defend the doctrine of a bodily resurrection. Several Christian works from this period argue against the idea of a spirit-only resurrection on the grounds that if only the spirit rather than the body as well were rewarded or punished at the final judgment then that would be unjust since the body participated in the deeds during this life it ought to be punished or rewarded too.

the apostolic teaching is that the soul, having a substance and life of its own, shall, after its departure from the world, be rewarded according to its deserts, being destined to obtain either an inheritance of eternal life and blessedness, if its actions shall have procured this for it, or to be delivered up to eternal fire and punishments, if the guilt of its crimes shall have brought it down to this. (Origen 230AD, First Principles, Preface 5)

In short this trio of doctrines are interconnected and seem to be the universally present in virtually all the writers of this period. (Offhand I can't think of any they aren't in, and certainly no orthodox writer in this period actively denies any of them) Together they form what I would call the "system of salvation" or "atonement theology" of the Christians of this period.