First you have to know your goals. What qualities do you want him to bring to the flock? Are you going to be hatching eggs or is he there for some other reason? Are you going to show chickens? Are you after eggs, meat, or something else? The perfect rooster will be different for each of us because we have different goals.
My goals are a black mottled or red mottled chicken (various shades of red) that lay green eggs. I hatch my own eggs. The chicken’s primary purpose is for meat, the eggs are a nice byproduct plus I need them to hatch. I prefer a broody hen to using an incubator and brooder.
My perfect rooster is red mottled, I’ll keep the black in the flock with some of the hens. He should have the blue egg gene. Since there are only two of us I don’t necessarily need a huge rooster for meat, but I want one of decent size and, more importantly, fast maturing.
Since I want fertile eggs and a peaceful flock I want a rooster that can dominate the hens. He needs to keep peace in his flock and the hens need to respect him enough that they willingly submit to his advances. A weak rooster that can’t dominate the hens and win their respect leads to brutality in the flock, just as a hen that will not accept a good rooster leads to brutality and unrest in the flock. He needs to dance for he hens, find them tidbits of food, keep the eggs fertile, and keep a good watch for danger. A good rooster will check out suspicious circumstances but once a real danger has been identified it’s fine with me if he leads his flock to safety instead of remaining between them and the danger. By checking it out and warning the flock he has done his job.
No human aggression is tolerated, other than when he is just reaching maturity as flock leader and tries his limits. He needs to learn his limits pretty quickly. I prefer him to have hatched from a hen that goes broody so he can pass those traits on to his offspring. I’ve never had a mature rooster threaten a chick in any way, more often they help Mama with the chicks, but any threat to a chick would not be tolerated.
That’s basically it for me. Others will have entirely different criteria. Most important of all, you have to know what you want before you can identify it.