I'm trying to get my head around this idea of original sin...
*Is original sin a core Christian idea?
*What is the scriptural basis?
*Does it mean that we are already regarded by God as having committed sin even before we are born... or does it mean a proclivity for sin, a sinful nature?
It is shown in scripture that our nature is one that moves toward sin when left to itself.
Gal 5:17 For the flesh lusts against the Spirit, and the Spirit against the flesh; and these are contrary to one another, so that you do not do the things that you wish.
Mat 26:41 Watch and pray, lest you enter into temptation. The spirit indeed is willing, but the flesh is weak."
As for the idea of original sin, it has various meanings for various people. Some talk of a thing called "Totally Depravity". Total Depravity is a thought that no one "Wants God", or can not "respond to God's message", so God pulls some out of that state to save. This then introduces a thing called Predestination, some think God knows all people before creation and selects a few of them to save. Like God writing a story, it denies true free will. Others like myself believe in the free will of man, or the idea that, although man is in a state of sin, God opens their eyes to Himself, and asks them to turn from sin, the response of the person determines their outcome.
Job 36:10-12 He openeth also their ear to instruction, And commandeth that they return from iniquity. If they hearken and serve him, They shall spend their days in prosperity, And their years in pleasures. But if they hearken not, they shall perish by the sword, And they shall die without knowledge.
John 14:21 He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him.
Freewill is also supported by the early church fathers.
Justin Martyr [A.D. 110-165.] - First Apology - Ch 56-50
Chap. XLIII — Responsibility Asserted.
But lest some suppose, from what has been said by us, that we say that whatever happens, happens by a fatal necessity, because it is foretold as known beforehand, this too we explain. We have learned from the prophets, and we hold it to be true, that punishments, and chastisements, and good rewards, are rendered according to the merit of each man’s actions. Since if it be not so, but all things happen by fate, neither is anything at all in our own power. For if it be fated that this man, e.g., be good, and this other evil, neither is the former meritorious nor the latter to be blamed. And again, unless the human race have the power of avoiding evil and choosing good by free choice, they are not accountable for their actions, of whatever kind they be. But that it is by free choice they both walk uprightly and stumble, we thus demonstrate. We see the same man making a transition to opposite things. Now, if it had been fated that he were to be either good or bad, he could never have been capable of both the opposites, nor of so many transitions. But not even would some be good and others bad, since we thus make fate the cause of evil, and exhibit her as acting in opposition to herself; or that which has been already stated would seem to be true, that neither virtue nor vice is anything, but that things are only reckoned good or evil by opinion; which, as the true word shows, is the greatest impiety and wickedness. But this we assert is inevitable fate, that they who choose the good have worthy rewards, and they who choose the opposite have their merited awards. For not like other things, as trees and quadrupeds, which cannot act by choice, did God make man: for neither would he be worthy of reward or praise did he not of himself choose the good, but were created for this end;52 nor, if he were evil, would he be worthy of punishment, not being evil of himself, but being able to be nothing else than what he was made.
Irenaeus [A.D. 120-202] in his Against Heresies - Book 4 Ch 35-38
5. And not merely in works, but also in faith, has God preserved the will of man free and under his own control, saying, “According to thy faith be it unto thee;” (Mat 9:29) thus showing that there is a faith specially belonging to man, since he has an opinion specially his own. And again, “All things are possible to him that believeth;” (Mat 9:23) and, “Go thy way; and as thou hast believed, so be it done unto thee.” (Mat 8:13) Now all such expressions demonstrate that man is in his own power with respect to faith. And for this reason, “he that believeth in Him has eternal life while he who believeth not the Son hath not eternal life, but the wrath of God shall remain upon him.” (Joh 3:36) In the same manner therefore the Lord, both showing His own goodness, and indicating that man is in his own free will and his own power, said to Jerusalem, “How often have I wished to gather thy children together, as a hen [gathereth] her chickens under her wings, and ye would not! Wherefore your house shall be left unto you desolate.” (Mat 23:37, Mat 23:38)
*If God punishes us, is it for sin or for a proclivity for sin?
God gives each person light, or knowledge of Himself. He then asks that we turn from sin to God. Our response determines where we end up.
Joh 1:9 That was the true Light which gives light to every man coming into the world.
Rom 2:4-11 Or do you despise the riches of His goodness, forbearance, and longsuffering, not knowing that the goodness of God leads you to repentance? But in accordance with your hardness and your impenitent heart you are treasuring up for yourself wrath in the day of wrath and revelation of the righteous judgment of God, who "WILL RENDER TO EACH ONE ACCORDING TO HIS DEEDS": eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality; but to those who are self-seeking and do not obey the truth, but obey unrighteousness—indignation and wrath, tribulation and anguish, on every soul of man who does evil, of the Jew first and also of the Greek; but glory, honor, and peace to everyone who works what is good, to the Jew first and also to the Greek. For there is no partiality with God.
*Does Jesus' sacrifice cover our sins, or our proclivity for sin?
Both.
Gal 5:13-14 For you, brethren, have been called to liberty; only do not use liberty as an opportunity for the flesh, but through love serve one another. For all the law is fulfilled in one word, even in this: "YOU SHALL LOVE YOUR NEIGHBOR AS YOURSELF."
Gal 2:21 I do not set aside the grace of God; for if righteousness comes through the law, then Christ died in vain."
Gal 5:16 I say then: Walk in the Spirit, and you shall not fulfill the lust of the flesh.