I just looked back at my records. My barred Rocks and Easter Eggers were the first ones in my flock to start laying. First BR egg was at 21 weeks. The second BR started laying at 23 weeks and then my EE joined the club at 24 weeks.
Don't expect to get eggs until 6 months and you may end up being pleasantly surprised a little earlier. All the breeds you mentioned are breeds (well EE's not a breed) that come to point of lay at the earlier end of things, but there are a lot of factors including their general health and living environment and just the genetic make-up and health of the individual bird. Just like people, birds start ovulating at slightly different ages. 6 months is considered the norm for chickens, though some cross-breeds may start as early as 15 or 16 weeks, and some heavy breeds not til closer to a year.
The first egg is like a present. You will feel like you gave birth or something. Waiting can be agony, but sooner or later you will be there. There is a first egg thread that is lots of fun when you get closer to the 6 month mark. Hope you don't get too impatient waiting.
ETA Don't expect them all to start laying at once. My flock took 2 months from the time the first one started til the last one started.
