A breeder looking to raise show steers, or calves in general, should breed cows for quality and consistency. This can be achieved by taking into consideration your cowherd and traits you desire from the AI (artificial insemination) or herd bulls available. Using bulls with a proven breeding record of producing quality cattle, producers should also desire consistency in their animals whether the animal be for show or commercial purposes.
Trial and error will come into play at the start until a breeder finds which bulls click on his or her cows. Pedigree and desired traits definitely need to be considered, however, and also dominance of traits like homozygous polled, color, disposition & calving ease.