Line breeding usually refers to mating the progeny back to the superior parent. If the parent is not any better than the progeny there is no reason to do this. Advances are made if you have a superior bird and you want to make more of that type of bird. If all you have are mediocre birds you really shouldn't consider line breeding. Line breeding has negative effects on reproductive traits and if you can avoid it you probably should.
Line breeding is usually done by crossing a sire to his best daughters or crossing sons back to their dam. The reason to do this is if the parent is very good in aspects that you want in your line. If the parent has defects you obviously do not want to use it for further breeding if you do not have too. Line breeding works because it puts more of the superior genetics of the parent into your line. If the bird is a bad example of the breed you do not want to line breed it.
Take a male example: you have a superior cock and cross it to a number of good females. You don't have to keep an initial pedigree because all the progeny will have half the sires genes and half from one of the hens. You take these daughters and cross the best ones back to the superior sire and now the progeny have 75% of the sires genes instead of 50%. They get a 50% from the sire and since the daughters already have 50% of their sires genes they contribute the other 25% (half of 50%). You can continue to backcross to the superior parent until you start having fertility problems, but after two backcrosses (3 generations with that male) the genetic returns are not improved very much. The first cross you have 50%, the first backcross you have 75%, the second backcross you have 87.5% and the third backcross you have 93.75%.
Line breeding gives you a better chance to recreate the superior bird, but the chances are still not good because it only increases the chance and the chance is not really that great. It is the best way to improve the line for a complex genetic trait if you do not know what you are selecting for except the final phenotype (what the bird looks like). You can think of it this way even though by the third backcross 93.75% of the genes (on average) come from the sire, animals have two copies of every gene and the copies can be different so that at every gene that the male has different copies of the same gene you have only at most a 50% chance of recreating that combination in the backcross progeny, so if only 4 genes have two different copies you have only 1 out of 16 chances to recreate that genotype. The bird has thousands of genes. Only a fraction are important to your selection, but that is still a lot of genes.
If you just want to amplify your stocks so that you can start a regular breeding program you may want to maximize your initial genetic diversity. Pedigree the chicks if you can by their dams and next generation breed the dams back to cockerals that you know are not their son's. This minimizes inbreeding for the first two generations and should allow you to generate enough birds to select from to start up a couple of mating pens. If the sire isn't an exceptional animal I wouldn't use him in the second generation unless I had to. Already half of the genes in the new generation come from him. If you use him again you will only make your line more like him.
Assuming the cock is a good bird or the daughters are better than the mother then you would breed the father to the daughters and maybe make a separate mating with the hen. If the cockerels from the hen are better than the cock you have then breed one back to her next year. You dont want to do it too many times. Also, remember that the best show birds are not always the best breeders. For males in columbian, a standard colored male with hens with good undercolor and maybe some smut near the tail for females a standard colored female with a male with less black in his saddle all should have good black markings in there wings with no tendency toward brown. Choose breeders with the best type possible. Assuming the male's shape is good, if his wings are light breed him only to any daughters who have good wings . Whatever defects they share will be magnified in the chicks.
