Glad I may be saying something of use.
Regarding breeding, there's no need to discard some hens around breeding season because you've chosen to not breed them, they may come in handy as egg suppliers while others are brooding, or other random helpful uses. I usually have some non-breeders who earn their keeps well and thus aren't culled. I've not been thrilled with the quality of the purebreds from various breeders I've tried, and my focus has turned to mongrels and I'm working on my own breed.
I've got many different chickens of many breeds and mongrel mixes and am breeding primarily for useful traits under the old guiding axiom that 'no good cow is a bad color.' I figure once I've locked the traits I want in, I'll put more emphasis on refining the aesthetic side of the genes. My criteria are: they must be useful for or showing potential strengths in at least one of the following: dual purpose production, good feed economy, maternal instinct, hardiness, and lack of or small amount of non-serious undesirable genes. Each chicken is rated on a mental score for the points it gets for how many of the desirable traits it carries. There is one crucial rule I don't allow any bird to breed in defiance of; if it isn't nice natured and calm and nonviolent, it's gone. This showed immediate results in the gentleness and calmness of all the random birds hatched from then on, but I think good nutrition and freeranging to their heart's content has a lot to do with it too.
Other factors I breed for are good feathering and I've removed leghorns and white pekin/silky genes as well as some strains of black australorp almost entirely from the flock due to leucosis. I've ended up with many bizzare birds in the interim but currently have mainly silver dorking-like/welsummer/jungle fowl coloration, not actually recognisable as that just in terms of the patterning types. They're beautiful and chicken theft is booming in Aus! I've had my best two stolen.
I set such loose parameters to begin with as I'm breeding things as diverse as silky mixes to layer hybrids to heritage mixes. Gradually, actually surprisingly quickly, I wound up with a general standard outline of the bird that carries these qualities I'm after. They're getting huge though and I may breed more banty into them, but they're extremely feed economical and the best girls I've been producing lately are prolific layers and great mothers. Both genders are very plump but not fat, the meat quality's really getting tender and juicy and nicely flavored in the latest generations. On that note silkies can contribute black flesh and bones which are usually considered medicinal, the flavor's fine, but for the sake of the easily grossed out I've bred back to whiter meat.
Some random traits I've encountered in chickens I've not heard of prior to keeping them: they can have vastly different colored eyes, anything from black to blue to green to red to yellow to white, or two-toned like red irises with green rings around the pupils, or black rings around the irises. They can have each eye a different color. They can have noodle feathers, not frizzle or silky but tightly curled proper feathers with corkscrew spirals. Like soft smooth dreadlocks. They can have double claws, as in the toe is extra wide with an extra wide claw with a depression showing where it wanted to be two toes. (That's from the extra toed bloodline of course). Females can grow proper spurs and crow and mate with other females and still be great hens. They can have claws like cats in their wings, at the frontmost joint carried closest to their breasts, not the shoulder, nor the 'elbow', but the 'wrist' joint, a bit like a hoatzin; it ranges from a sharp straight forward pointing spur to a proper realistic cat's claw of the same size, or even two per wing, and they use it in fights and to hold onto nests and stuff. (They start to lift the nest with them once you try to check the eggs after they've got those claws). Also they can grow straight backwards pointing spurs as long as their proper leg spurs from the same wing joint which they stab with. This grows well and truly before their leg spurs have gotten adult length, and is anchored on bone and fully usable. I theorize this is actually a more primitive trait and the reason roosters as well as angry hens hold their wings in that tilted position: it's a visual threat to stab, adopting a velociraptor pose because they are in fact armed about the same. Also, they can grow multiple leg spurs. Also, eggs can hatch at 14 days. Eggs can be left to freeze through winter and survive on half an hour's heat a day and still hatch. They just take weeks longer to develop because of how long they spend in suspension. This is all true, though I wouldn't blame anyone for not believing me! I'd never heard of it all myself before trying to breed my own. Edit: I forgot: some chickens have rainbows on their feathers. These can be oil-spill style, blended perfectly, or striped without blending the colors. The colors include purple, green, pink, gold, blue, and red. This shows best on the black parts of the feathers because it is sheen rather than actual pigmentation.
I don't select for egg color, only quality. Also it shouldn't be too small nor too big relative to the hen's body size, and due to the risks to the hens I no longer breed those prone to two eggs a day or double yolkers. It's harsh on them. The egg should be glossy and strong shelled with a rich bright orange yolk and strong jelly like white, preferably yellowish tinged. If its watery or the yolk's pale, you've got either an unhealthy bird or one who genetically hoards the nutrition to herself. Layer breeds and their hybrids are classic examples of that, they tend to produce bigger but weaker and inferior eggs. More water, that's all. Many bantams have the same sized yolk in their half-the-size egg, and when their chicks hatch they practically burst from the egg whereas bigger eggs often produce bloated and weakly and slow chicks who take a day or several to get up and around. The egg type that's appearing more often now is pinkish or dusky rose, often with white or purple spots, which is pretty.
Watch for incorrect leg scaling because that will lead to 'outie' or 'innie' spraddlers. You can't fix these because unlike proper spraddling this is an anatomical deformation. They will usually gain their feet after a week or so but will always suffer for it. Breeders often give you birds to breed with bad legs without saying why. Nor do the books tell you. I found out the hard way. Now I can check a newly hatched chick and know if it's a culler or not. Which is a sad thing to have to weed out of your flock at a later date so I urge you to check their legs and make sure you don't breed any misaligned leg scaled birds. The parents may walk fine but the babies won't; it's recessive but only just, and one parent carrying the trait is too many. I may be an idiot for this but I dig those wing claws and spurs so much I want to keep breeding them into my strain; they did in fact pop up on my best birds and appear to come with the traits I'm after so it would be hard to weed it out, and since it was always the nicer birds that had them, I'm hoping it's not a potentially dangerous choice --- breeding chooks with more weapons! :/ But it's so fascinating...