The largest and plumpest I roast Zuni Cafe-style, which makes a pretty good dinner for three or four people.
The other three I cut up and divide thus: chicken wings (tips go into the stock pot); skinless chicken thighs (perfect for mole or gumbo); skinless whole breasts; livers, to be sautéed and then saved for Cajun boudin or dirty rice; and everything else goes into the stock pot.
To make a good rich stock, about 3 quarts from the trimmings, I season the pot with a little salt; peppercorns; a bay leaf; the middle of a celery stalk, with leaves; and a carrot or two; then cover with water. This is brought to almost a boil, then turned down low to simmer, usually overnight, or until the meat is close to falling off the bones. After cleanup from the Zuni chicken, I throw the drippings and whatever bones are left into the pot, too.
I usually drain the stock while it is still warm, but don't strain it through cheesecloth until I need to for certain recipes. I chill it and skim off the fat (I save the schmaltz for a while, in case there's some cookbook recipe that calls for it, but I usually end up pitching it, since I limit the amount of animal fat in my diet). I measure out the broth in several size containers: 1 cup, 1.5 cup, 2 cup and 3 cup; then I label and freeze.
Then comes the most time-consuming part: I pick out any choice meat that's left, which is usually about a quart bag full, and label it for a later chicken soup. That goes into the freezer, too, unless I'm making soup that day.
If you aren't taking out your garbage in the next couple of hours, put the remains in a bag and freeze it. Then dump the frozen bag in the garbage when you take it out.
I've tried to get my cat interested in the gizzards and hearts, but so far, no luck. I use a lot more of the chicken when I have a dog.