Out of my first flock, which were Easter Eggers, (Amareucanas), Barred Rocks, and Rhode Island Reds, our barred rocks are skittish, and our rooster was mean. One of the Rhode Island Reds was very sweet as a chick and my son handled her a lot. As they got older, I have one Easter Egger we've named Hawk, and she's a character, very independent. Though they were just layers and not handled a lot, she would walk up to you. When she's in the mood you can walk up and catch her no problem.
I've got a second flock I'm raising, and I've got another Easter Eggers, who's a real sweetie. If you want a pet that's also a good layer, I suggest Easter Eggers. Mine lay through the winter and produce the largest eggs out of my flock. They seem to be really hearty too. I've lost several Barred Rocks, but not a single Easter Eggers.
If you want a good pet just as a pet, I'm really enjoying my new silkie chicks. They fall asleep in my lap. I'm going to have a hard time putting them outside when they get older.