The Struggle Between God in the Old Testament and the New
I understand and sympathize with your challenge between the Old and New Testament stories of God. I have struggled with many stories of God's wrath, retribution and justice.
The harder part is that God, including Jesus is often presented this way in the New Testament too. We see Jesus practically condemning leaders and whole towns. We see him called Peter Satan. We see him talk about the coming wrath and hardship (especially for Israel the chosen, "favored people"), and we see similar things in Acts, the letters, and in Revelation (revelation even more so), but it is less prevalent for a really important reason because, through the birth, death, and resurrection of Jesus Christ and the giving of the Holy Spirit, God is transforming people.
I would agree the New Testament is more about forgiveness, mercy, and welcoming the downtrodden. This is God's ultimate purpose and goal, even in the Old Testament, and his purpose for his followers to practice too. Jesus as God become human embodied God's purpose for humanity in an absolute way; many call him the first full human because of that. Jesus even tells us that he did not come to judge, but rather to deliver. Yet, we know God is the only righteous judge and it is that which we struggle with in the OT. The hard part is that his judgments seem a lot more intense than his forgiveness, yet his forgiveness is strong and liters practically every story, but because of the nature of forgiveness (freeing from at least some repercussion) it can almost disappear unless we are conscious of it or someone calls it out. Because of the nature of forgiveness, we often don't know the full repercussions of our actions, people in older generations I think a better understanding of this. What the OT faces us with is that our actions are more monstrous than we can imagine and to create justice and to restore the world something extreme needs to be done; Jesus, the Son of God's death was practically the most extreme thing I can imagine.
Through all of humanities actions, justice and retribution needs to be accomplished. We cannot be left to the full consequences of our continuous evil actions and so God has to continually step in to set things right - this is both mercy and justice, but it is hard for us to see sometimes. The hard part, especially with the old testament is that these writings don't often spell out God's reasoning or even the situation. It is designed as meditative literature that is meant for us to take time on and really contemplate and wrestle with. When we come up against something that seems wrong to us, we are meant to spend time with and reflect on it with everything else we know, even looking way back in Scripture (or sometimes forward). We can often take God's earlier images, desires and purposes for us to help us understand why something seems to be the opposite. If Abraham and his family were meant to be a blessing to all nations, how come in this moment it seems to be the opposite? Or if all of humanity was meant to be fruitful and multiply, then why in this moment does it again seem to be the opposite? If God ordered creation to help life flourish, why does it suddenly seem like disorder, chaos and/or life is not flourish? Usually the question is what are we or the others not doing or doing wrongly?
These are not easy questions, but they are very real and pertain to all of our life, especially when we are experiencing the same thing.
There are some further ideas to help clarify these things: how does God relate to or participate in natural consequences? In my experience he most often saves us from full consequences or mercifully redeems them, but sometimes he does allow full consequences or even will speed up the consequences to show us the result of our evil actions or culture (I think the flood is an example of this and I think the Exodus portrays almost all of these).
When looking at favoritism, look at how God punishes both Israel and the nations surrounding them. What is different, what is similar? God often holds Israel more accountable, because he has higher expectations for a group in a covenant relationship with him.
When it comes to God forgiving Israel more. I think that is true. God is in a committed/covenant relationship with Israel. He will do a lot to maintain a strong relationship that has already been built and live into his promises to them. Though God will also judge Israel more severely too, expecting more from them in their favored position. We can see both of these at work in their journey through Exodus. What we also see though, is that God wants to invite more people, even those outside of Israel, into this covenant relationship. As with the promise to Abraham this includes blessing those that bless Israel and cursing those who curse Israel, though this actually a natural consequence in all situations, I think it is especially true with Israel.
Each moment in Scripture is trying to present something in a little different way, often building on previous ideas, so it would be impossible to go into everything, but I thought this might be a helpful place to start.
