I agree that if you start with a friendly breed and handle them a lot, it'll go a long way toward them being friendly when full grown.
Like you, we are raising our gals in a small backyard (25' X 64') and are limited by city code to just a few. We went to the local feed store and the kids selected 2 RIRs and an EE. The kids were involved in the process from the very beginning, from reading Gail Damerow's "Your Chickens: A Kid's Guide to Raising and Showing" to painting the coop and helping to build the run, to daily chicken chores.
From the moment we brought them home, the kids have been involved in their care so they're very comfortable around the girls and vice versa. Of our three, the EE is the least friendly, but amazingly she LOVES our 12 year old son. He can carry her anywhere and she just snuggles with him. She'll let our 10 year old daughter carry her as well, but I think he's her favorite.
The girls will be 2 years old in late March and the kids have never grown tired of them. I hope that whatever girls you choose, they'll be as much as an asset to your family as our girls have been to our home.
Edited to add: I also keep a chicken calendar. To answer the egg laying question. From point of lay to one full year later, one RIR laid 307 eggs, one RIR laid 301 eggs, and the EE laid 214. That's OK that Elsie the EE isn't the best layer. . . She's soooo pretty!