I place my kittens between 12 and 16 weeks of age. This makes sure their immunizations are done to my standards. The kitten may be already neutered if male, unless planned for breeding. The females may be spayed, assuming the normal state of health at that age. By this age, they have a good footing in social manners including box use, scratching post use, grooming, nail trimmings, teeth brushing, and possibly bathing. If certain things are wished, such as leash training, we can also spend time with that in the comfort of Mom's presence.
I also consider their emotional health and maturity before placement. By 12 weeks, they are quite independent and can be placed if not a rumpy. The rumpies stay until 4 months to be sure of their health.
I place retired breeders in loving homes so they can have the luxurious life of a pet. My lap is only just so big and I feel they all deserve their own lap after their contributions to the preservation and betterment of their breed. Some may need to be the only cat, some may really need a buddy to roughhouse with. It's usually easy to know if a certain cat will work in a particular situation. I love to hear how their personalities blossom when they own their own family!
These ones who have been with me longest are often the ones I find hardest to part with, they sure grow on you! But I find comfort in knowing I am sending them to a lap devoted to them. I strive to send them already altered, with clean teeth and a health exam. Bloodwork may have happened depending on the age of the cat.