The Holocaust was extraordinarily important for the Israeli psyche. There was, especially in the first two decades of the state, a huge tension at play. On the one hand, Israel was founded under the idea of sabra dominance and Israeli machismo of a sort. Zionism touted the idea of a Jew who was no longer at the whim of other nations and states, and powerful for the first time. A state was seen as the ultimate example of Jewish power and ability: a way to say "Look, we will not allow atrocities to occur again" (this ideology preceded the Holocaust, for the record). The Zionist Jews that later founded the state, like the first Israeli Prime Minister David Ben-Gurion, came in the Second Aliyah. This movement of people, from 1904-1914 roughly, made up only around 25,000-30,000 people by most estimates, but the ideology it brought (left-leaning and borderline socialist, and the idea of strong young men moving to settle in the region that would become Israel) lasted in future generations.

So this machismo, this whole image of a strong young Jew who would fight and plant and build the new Jewish state, was challenged by the Holocaust. On the one hand it was a perfect example of the need for this Jew. On the other, Jews found themselves questioning how something like this could happen. How could the world, how could they have allowed this to happen? Where were the fighters? Where was the rebellion?

So Israel, in its founding mythology and as part of its national consciousness, mostly eschewed honoring Holocaust survivors in totality. They were treated poorly, as people who submitted to the Nazis and failed to stand up for their identity. Only those who fought, as with the Warsaw Uprising and other groups like a specific kibbutz (Lohamei Hagetaot, the Ghetto Fighters) founded by former fighters of groups that fought the Nazis and their children, were seen as legitimate Israelis. It was a way of dealing with the collective embarrassment of failure to act, and brush under the rug as it were the way Jews were led to the slaughter like sheep without organizing themselves to fight.

After 1960 or so, there was a shift away from this ideology, but that's another story.

Regardless, genocide and the Holocaust clearly played a huge part in Israeli ideology. And that is why Israel was so concerned with morals in the case of, for example, the Adolf Eichmann trial. Israel did not have the death penalty, viewing it as illegitimate and cruel, but it made an exception for Eichmann because of the severity of his crimes in the Nazi regime. The idea of repeating the Holocaust or committing a genocide was never something Israel seriously considered it would do, and while I'm happy to challenge those who claim it has done so in the past or is doing so now, that is a discussion for elsewhere. That discussion is on history taking place in the past 20 years, which is not allowed in this subreddit.

As far as what precautions Israel took, if there were any, Israel signed multiple international covenants and treaties binding it to a commitment both defining and examining the crime of genocide. Israel signed and ratified, without any reservations, the 1951 Convention on the Prevention and Punishment of the Crime of Genocide (entered into force in 1951, passed by the UN General Assembly in 1948). It has ratified the Geneva Conventions, which classify civilians as protected persons and thus de facto would make it impossible to commit genocide without heavy violation of the convention. Israel ratified the Genocide Convention in 1950 by passing this law, which gives Israel a claim to universal jurisdiction, meaning that if a genocide was committed in Germany (i.e. the Holocaust) and Israel caught a perpetrator, it could try them in Israeli courts just as if the genocide had been attempted against Israel.

That about sums it up, I think, unless you have more specific questions on the topic.