Modern Christians have various ideas of salvation since Jesus came (going to heaven when you die; free from the curse of the law; set free from the flesh, the devil and the world; adopted into God's family, etc.).
What did salvation mean to the Israelites of the OT?
Throughout the narrative parts of the Old Testament, there is very little mention of any afterlife. That idea arises mostly later on, in the books of the Prophets.
During the bulk of Old Testament times, salvation had little or nothing to do with:
And as for being set free from the world, it was just the opposite. As we will see, salvation meant being blessed in the world.
Of all the possibilities raised in the question, only being adopted into God's family has any real bearing on salvation as understood by the ancient Israelites. They saw themselves not exactly as God's family but as God's people. So in that sense, being God's specially chosen people does relate to their concept of salvation.
Now, if few to none of the common Christian understandings of salvation had any meaning to the ancient Israelites, what did salvation mean to the Israelite people of the Old Testament?
Quite simply, to them it meant literal, physical salvation from human enemies, and from material-world "enemies" such as poverty, disease, and death. And on the positive side, it meant having wealth, power, and victory over their enemies, all of which were seen as blessings from God.
In the Hebrew Bible, aside from a poetic use Genesis 49:18, the first use of the word "salvation" (יְשׁוּעָה, yĕshuw`ah) occurs in Exodus 14:13-14:
And Moses said to the people, "Fear not, stand firm, and see the salvation of the Lord, which he will work for you today. For the Egyptians whom you see today, you shall never see again. The Lord will fight for you, and you have only to keep still."
The scene is the Israelites camping by the Red Sea, and the Egyptian army pursuing them with horses and chariots.
The salvation of the Lord was the Lord's drying up the sea so that the Israelites could pass over on dry ground and escape from the Egyptian army, and then the Lord's closing the waters back over the pursuing Egyptian army, drowning and destroying them, and thus saving the Israelites from their power.
So here in the first narrative use of the word "salvation" in the Old Testament, it means God saving the people from literal, physical, human enemies who were bent on recapturing and carrying them back to slavery in Egypt.
This use of "salvation" as being physically saved from human enemies is common throughout the Old Testament. For a few more examples, see Judges 7 (note the word "saved" in verse 2); 1 Samuel 11 (note "salvation" in verse 13); 2 Samuel 23:8-12 (the word "victory" is a translation of the Hebrew word for "salvation").
When speaking of the people as a whole, then, for the ancient Israelites "salvation" meant especially being saved from enemies who wished to kill, conquer, and enslave them. "Salvation" was synonymous with victory in battle against enemies.
Less commonly, "salvation" was used of individuals who were saved from sickness, enslavement, loss of property, death, or other material calamity.
For example, the prayer of Hannah, the mother of Samuel, in 1 Samuel 2:1-11, which celebrates the Lord's salvation of her from the terrible condition (for an ancient Israelite woman) of barrenness, opens with these words:
And Hannah prayed and said,
"My heart exults in the Lord;
my horn is exalted in the Lord.
My mouth derides my enemies,
because I rejoice in your salvation."
And David's song of praise in 2 Samuel 22 similarly speaks of the Lord's salvation (mentioned specifically in verses 3, 36, 47, & 51) not only of his people and his army from their enemies, but of himself (David) personally from Saul's attempts to kill him because he was rival aspirant to the throne.
So whether it is speaking of the nation as a whole or of individual people, "salvation" in the narrative of the Old Testament most commonly means salvation from and victory over physical, human enemies and over material-world sufferings and setbacks.
By extension, the Lord's threats and promises to the Israelites almost invariably involved physical and material ruin, defeat, and death on the one hand, vs. victory, health, prosperity, and long life on the other.
The narrative of Deuteronomy 26:16-30:20 is a long series of physical and material curses, defeats, and calamities that would befall the Israelites if they disobeyed God's commandments, and of blessings of victory, health, and prosperity that they would enjoy if they obeyed God's commandments. It concludes with these famous words:
See, I have set before you today life and good, death and evil. If you obey the commandments of the Lord your God that I command you today, by loving the Lord your God, by walking in his ways, and by keeping his commandments and his statutes and his rules, then you shall live and multiply, and the Lord your God will bless you in the land that you are entering to take possession of it. But if your heart turns away, and you will not hear, but are drawn away to worship other gods and serve them, I declare to you today, that you shall surely perish. You shall not live long in the land that you are going over the Jordan to enter and possess. I call heaven and earth to witness against you today, that I have set before you life and death, blessing and curse. Therefore choose life, that you and your offspring may live, loving the Lord your God, obeying his voice and holding fast to him, for he is your life and length of days, that you may dwell in the land that the Lord swore to your fathers, to Abraham, to Isaac, and to Jacob, to give them. (Deuteronomy 30:15-20)
As shown in the entire narrative sequence that concludes with these words, the life and death, good and evil that the Lord set before them was physical and material life and death, good and evil.
For the ancient Israelites, then:
The more abstract versions of salvation and damnation that came later, in the Prophets and especially in the New Testament, used these earlier pragmatic and earthly meanings of salvation and damnation as symbols and representatives that foreshadowed and depicted spiritual salvation and damnation.
Before and even after the Incarnation, the Jewish people have considered themselves to be set apart (Holy). Set apart not by Works, or by lineage or even by Ethnicity, they were set apart, made Holy, by Covenants made by God with man. This action done solely by the Grace of God set the people of God apart from all others. They were God’s Chosen people, Chosen to do Gods will and Chosen for the Promises given to Abraham through Isaac.
How they interpreted this relationship with God, differentiated between different sects of Judaism, some believed in a bodily resurrection, some did not, some believed in the continuation of the soul after death, some did not. These differences exist even today in Judaism as many make a mark for themselves in this life and not in the next.
As Christians we have various ideas of what salvation is, so do the Jews of then and now. One thing however has not changed, that is how we perceive those covenants and apply them to ourselves but do not live up to them. I think of Ecclesiastes and the Vanity of Vanities, “There is no remembrance of former things; neither shall there be any remembrance of things that are to come with those that shall come after.” Ecc 1: 1-11 As the Jews were set apart, they saw themselves (presumed) as favored by God, many Christians who in the same manor consider themselves share this favored status, (being saved) by God presumptuously.
What it meant to the Israelite people of Old Testament was that Salvation to them, via the Law and the Promises of Grace to the seed of Isaac, was a forgone conclusion whatever eschatology they adhered to, Regardless of how they lived their lives. This vanity continues in Christianity today.
“If thou be the Son of God, cast thyself down: for it is written, He shall give his angels charge concerning thee: and in their hands they shall bear thee up, lest at any time thou dash thy foot against a stone” Math 4:6
compared to
“All you need to do is have faith and you will be saved, leap and worry not, for you are saved by faith alone, Christ will bear you up” (Reference Mine)
What is needed then and now, is to be aware of the sin of presumption. “Thou Shall not temp the lord thy God” Mathew 4:7