It's two heads of the same coin. Answer as you prefer.
Origin of Evil:
Well, my theory as to where evil came from: is that it was a byproduct of God's creative process. "Evil" is the opposite of everything God is; except it is not omniscient, omnipotent, omnipresent, eternal or immortal. (OOOEI)
"To every action is an (equal) and opposite reaction."
The action of God creating produced a creation that was not omniscient, omnipotent, omnipresent, eternal or immortal either. And the fact that this reaction was the opposite of God's action, (as opposed to the opposite of God's essence) is what limited "evils" capacity to the created realm.
Now all that God created He called "very good". It was pleasing to God, it was moral, it was beautiful (still is in many ways), and reflected these loving attributes of God. Evil though, is the opposite of all of that!
So God knowing that as soon as He created something, this is what would happen - this I believe was the "knowledge of good and evil" that God possessed. Now obviously God being the entity that He is; (OOOIE) could not be corrupted by that knowledge. But because the creation is not OOOIE, it is corruptible by that knowledge.
So in enters "tree of knowledge of good and evil". Evil existed in Adam & Eve's environment, they just didn't know about it. And since Adam and Eve are created in God's image but are not OOOIE; as soon as they transgress, the "proverbial stinky stuff" hits the fan and the entire creation is plunged into the control of evil. Evil now rules and this is what "the fall" is!
Now the atonement is the only way to not only pay for human sin, but also to get rid of that evil by making the Creator part of the creation. Now this is pretty awesome because becoming incarnated permanently alters an aspect of God's existence in that now an incorruptible created realm is forever needed for the incarnated person of the Godhead. And here is why there is a new heavens and new earth.
God would not create a universe that He knew to be fundamentally unredeemable. This is a demonstration of His love. Besides being loving, God is practical. He would not create something He knew as going to be eternally lost; there's be no point in that.
Besides that if God did not have the power to redeem what He'd created, He in essence would not be God and there'd be no discussion about this because we would not be here to discuss it; if that makes any sense to you?
Purpose for suffering:
God answers that for us. "All things work together for good to those who are called according to His purpose." The purpose God turns suffering into is for the advancement of the kingdom. What man means for evil, God uses for good.
Now from the perspective of the individual; we may never see on this side of eternity the full extent of how our suffering was used. Rest assured though, it was. This obviously requires trust in God to bring about His purposes from what ever our suffering has been.
Neither of these: (the theory on origin of evil or the purpose for suffering) make God responsible for suffering. It makes Him the counter agent of it.
Now does that make sense?