People usually say buff orpingtons and silkies are on the friendlier side, but keep in mind, every chicken is an individual. All depends on how much they were handled as chicks and in adulthood. Though some breeds like the heavy breeds and some bantams have a calmer disposition than high strung leghorns etc, making them an easier choice. Hope this helps!
I am in LOVE with my Dominique hen. She is very cooperative and friendly and intelligent too. She comes by name and is always the first to find bugs when she free ranges. My Cochin is also very friendly but her feet get very messy so I don't like it when she perches on my arm. My Faverolle clucks a lot when we pet her (she always has since chick-hood) but she is a sweetheart. I also really like my RIR. She lets me pet her waddle a lot and is calm and good for free-ranging. I also have a Wyandotte who is a little skittish and a buckeye who is a little on the aloof side. I would most highly recommend the DOMINIQUE, RHODE ISLAND RED, and COCHIN
I have read great things about silkies (they are a broody breed though so if you don't want that find a different bird). I have read several people posting that the silkies will follow them around or sit in their laps. Mine are still chicks but I have two in my lap right now! I also find silkies to be really cute!
Lots of people love Buff Orpingtons. I don't like them so much, but that's just me. Mine have been poor layers and not very friendly. We have one right now that we got specifically to tame as a pet and she lived in my basement for a while, but she's still not so sweet. The black Australorp and Amberlink that were in the pen with her are sweeter.
I've found my Australorps, Marans, and ISA Browns (a production hybrid) to be the friendliest birds I've ever had. Also, Red Sex Links (commercial names like Cinnamon Queen, Red Star) tend to be extremely friendly.