For the breed you are raising - check out all the qualifications in the American Poultry Association (APA) standard of perfection (SOP) and work with the ones that most closely match that. There are groups, associations and clubs for many breeds and they would be a good source for you.
IF there are any that are not as healthy as their flock mates- don't beed from them.
There are also specific traits that you may want - and if you aren't going for a particular breed - but have something like an Easter Egger, then you may want to go for a certain look or for the most intense egg color. If a chicken is mean---I would exclude that one from a breeding program unless there is something exceptional about that individual you need to keep. Of course if there are any chicken defects you would cull those chickens.
If you are going for the best egg-layer...and your eggs are all the same...you could use a 'trap' nest to know which one laid which egg and keep track by chicken and select her eggs.
For the meatiest, you could keep track of weights as they grow (assuming you would want fast growth so they can go into the freezer asap from hatch...then breed those? (I guess if they are in the freezer they won't be breeding--- lol, maybe someone on the meat boards could give help there??)
For my chickens, each has a different egg color, and their body types are different too....so it is very easy to know which is a good layer, and which will produce plumper chickens.... And good egg laying is a thing I will always be selecting for (among other traits)
Hands down my rhode island reds are amazing layers. Every day ! And my light brahama. My maran who is the same age 7 /8 months stopped laying -a month and a half ago. RIR/ameraucana lays every day to. My buffs nope, there to busy being broody lol. Will be getting more RIR's this spring
If you are looking to breed any given flock of chickens for meat or for egg production, I recommend reading "The Call of the Hen". You can find it online. The gentleman who wrote it goes over what traits to look for in your stock that will help you breed towards your goal.