Sounds like you have a reasonable plan. I don't know how good that breeder is about sexing chicks. Vent sexing is the only way with the Buff Orps and the RIR. It is not easy and the hatcheries only guarantee being correct 90% of the time. With the Barred Rocks it is possible to get a pretty good indication of sex if BR are the only ones in the brooder. The males are a lighter shade than the females, due to having two barred genes instead of the females having only one copy of that gene. So try to pick the darker of the BR and you will greatly improve your odds. It is not a guarantee but it is certainly the way I would go.
Picking unsexed chicks is just playing the odds. Each chick has an equal chance of being male or female. I once ordered seven straight run Buff Orps from Cackle and got seven females. It could have just as easily been seven males. I'm sure somewhere someone got seven males and is still bad-mouthing Cackle about it. In a recent hatch of 15 chicks, I had 10 females and 5 males. That hatch was mainly for meat so I wish the results had been the opposite. I can't tell you how many of each to get, just that you will very likely not get exactly what you want unless the breeder is very good at sexing.