Another thing you will need to consider is the individual cooking times of the meat, poultry and vegetables you use. They are all different. You can put them in at staggered intervals, first the meat, then the poultry and the vegetables last, so that everything will be finished cooking all together. I find this too difficult to gage with any precision, so I start everything together and remove things as they are done, which is much easier to tell by tenderness. I cook the vegetables peeled, but whole, and cut them up afterwards.
Parsnips even keep their tops until serving time.
I have made this dish with great gastronomic success using inexpensive chicken thighs and legs and chuck steak, when money was short. Years ago, when I worked for my father, I made it for the help, using short ribs and turkey wings which were byproducts. The chef told my father that I had a talent for making it, the best complement I ever got. Escoffier is said to have preferred to eat meat and vegetables from the stock pot instead of the elaborate rich cuisine he fed his patrons. As a matter of fact, one way of getting a rich flavor is to use some inexpensive oxtail in it.