What, in the end, is the story suggesting about this complicated concept? What brings people happiness?

In the end, the citizens of Omelas experience joy not because suffering exists but because they are willing to accept it as inevitable and ignore it.
In their perfect little society, the members of the community seem to have everything they need for a peaceful existence. They enjoy technology that is beneficial but not destructive. There are no soldiers and no kings. Their children roam the street with sticky faces.
Yet in the basement of one of the public buildings is a child, locked in isolation and deprived of human contact. The child suffers from extreme malnutrition and is mentally challenged:

Perhaps it was born defective, or perhaps it has become imbecile through fear, malnutrition, and neglect.

Everyone in the town knows the child is there.
The true horror is that everyone in the town lives with the knowledge of the suffering child. They have varying reactions; sometimes they leave in tears and sometimes in a rage. But eventually they learn to ignore the suffering so that they themselves can have joy. For some, this takes a little longer, and they brood over the situation for weeks. And then they learn to make excuses, telling themselves that this child could never be integrated into society anyway. Their sense of justice in keeping the child there becomes ludicrous:

Indeed, after so long it would probably be wretched without walls about it to protect it, and darkness for its eyes, and its own excrement to sit in.

The paradox is that to live in joy, they cannot acknowledge suffering. So they go about their lives, believing themselves compassionate, while they willingly allow suffering to underpin their happy existence.
The metaphor of the child representing universal suffering is one that can be applied to societies everywhere.

The story focuses primarily on what doesn't bring people happiness. Omelas is based on a philosophy that Le Guin critiques in the story: utilitarianism. This philosophy argues that a society is happy when it achieves the greatest possible good for the greatest number of people.
Omelas is a beautiful and pleasant place to live where everyone is prosperous except for one child, who is forced to live in misery and filth so that everyone else can be happy. But as the story shows, nobody can really be happy when their happiness is based on the suffering of an innocent child. Different people find ways to rationalize the situation, telling themselves that the child gets used to it or that it is a small price to pay for everyone else's good life. Yet once you know about the child, it is a like a horrible stain spread over the whole culture. It creates in the reader—and the citizens of Omelas, as evidenced by their rationalizations—a sense of unease.
Therefore, for all the beauty and pleasure in Omelas, it is not really a happy place. Some people can't accept this compromise and walk away from their culture. Without saying so, Le Guin implies that real happiness is only possible when suffering is alleviated for everyone. The people who have a shot at happiness are those who walk away. Their lives may be harder, but they will be living with integrity. On the other hand, as long as even one person is suffering, everyone is suffering—or at least falling short of being happy.