Generally speaking, there are about 8 or so atonement theories out there, with variants. To me, it’s easier to divide them into two groups.
One group of atonement theories postulate that the problems primarily stem from personal dimension of people (who are fundamentally perverse), and of God (who is fundamentally angry about people.) What Jesus did was more or less redirect the focal point of God’s anger to himself, thus getting us off the hook. The main idea is that of legal transaction.
The other group of atonement theories postulates that the problems to be solved are of systemic nature. They lie with both with human psyche individually (egotism) and socially (systemic oppression and scapegoating). There is also a cosmic dimension to the problem statement (decay and death). What Jesus did is he absorbed the individual, the social, and the cosmic sin (and therefore death), triumphed over them, and created a mechanism of being able to tap into the power to overcome all those.
I would submit to you that the second group of atonement theories has much more coherence and explanatory power. Also, the 2nd group is the one that leads you to living like a responsible, fully empowered representative of God in every area of life. It’s the only one that can underwrite consistently replicable results, and not just occasional haphazard “victories”.