Which breeds should be avoided together?
Many, depending on your setup and existing birds and kids and area.
If you don't have much space, you aren't going to want a pile of Production reds.
If you have a bunch of gamebirds, you probably don't want to add a silkie to the mix
If you have young children, I advise avoiding most commercial hatchery production roosters (Production Reds, Barred Rocks, etc.)
If you live in Northern Canada, you probably don't want straight-comb leghorns.
If you want long-lived birds, sex-links usually aren't the way to go.
There are exceptions to every rule, but there are no useless breeds--At some point, someone developed them for some purpose.