Welcome to BYC!
Like any animal of a breed there will be a big range of temperaments for the individuals. Breeding, handling and environment are big factors!
Like Cavemanrich stated there will be a pecking order and bossier birds will be at the top. I also have a mixed flock, although quite bigger than yours, so far my two week old Barred Rock Hen is mean when she is stressed out- like when the light has been on way past bedtime, but otherwise well behaved. She seems to be towards the top of the pecking order. She is also hatchery stock so I have no idea what her parents were like.
If you have plenty of space, food, water, and things to occupy the birds, along with good light/dark balance you should be fine with a barred rock. In fact if you don't meet these needs you will have issues with most breeds. If you are worried don't get one if you have extremely gentle breeds. There are also other barred breeds that may suit also.
Good luck with your chicken adventure!