The people they pick up and take home, the strangers/random people, I am guessing this psychotic person has found (in their thinking) something magical about them.

Being drawn to people for strange reasons, having ideas about them, could be either a personality trait in psychotic people, or it just comes from psychotic thinking. A vision quest.

They could appear special, meaningful, an omen, taking them home could have some magical effect on the house.

Why do they choose the people they choose, and get so excited about them, but the happiness/mood elation about these strangers could have no basis in reality, but rather, some other reality?

These are positive symptoms of psychosis, negative ones, are not so pleasant.

A lot has already been written in reply to this topic, I can't bring myself to read all of it. Bringing home strangers like a treasure hunt, or like pets carry home dead animals to impress their owners, it's cute. There's something so adorable about that.