After the stock, your next choice is which vegetables to use. I've already mentioned the classic onion, carrot and celery mix, but there are so many other choices available. From time to time I enjoy some chopped spinach in my chicken soup, or any other leafy green I happen to have on hand. Frozen peas are another great option, but remember to add them about 5 minutes before the soup is done cooking, unless you prefer your peas mushy. Tomatoes are another great vegetable to use in chicken soup, and they have the added benefit of bolstering a weak-tasting stock. You can also use "substitute" vegetables to replace some of the classics: fennel in place of celery, leeks or shallots for the onions, parsnips for carrots, etc. And let's not forget about all the peppers out there, both hot and mild!
When it comes to vegetables, I usually just add whatever I have in my refrigerator. Any leftovers or veggies that are about to expire become candidates. I usually avoid root vegetables as they take longer to cook through, but if they are already cooked then they are fair game too. If not, then just chop them up into small pieces so they cook more quickly.
Next in the list of ingredients to select is the type of starch to add. There are so many to choose from that there is no way I could list them all, but one thing to think of is how much the starch you choose will thicken the broth. This will depend on how quickly it dissolves into the broth and how long you will be cooking it for. Most people don't want to thicken their chicken soup too much, so pasta is the usual choice for most people. If there is one variant of chicken soup that is more famous than all the others, it would definitely be chicken noodle soup.
But noodles are far from being the only choice. Brown rice is my go-to starch for chicken soup. Like barley, it will thicken a broth given time, but it normally takes more than an hour for that to happen. I like how it swells in the liquid of the soup, and how it adds just a touch of viscosity to it. It helps the flavor of the soup cling to the tongue for just a little bit, enhancing the taste experience.
Lentils are a very healthy starch to use, and there are a lot of varieties to choose from. Red lentils will practically dissolve into the soup, while the little green gems known as Puy lentils will keep their shape almost forever. At the other end of the spectrum are potatoes, which given enough time will thicken a soup enough to stand your spoon in it.
If you want to go for big-time comfort food, then dumplings should be your selection. Personally I have never made dumplings, but I know some people that swear by it.
Lastly, you need to decide what spices and herbs to go for. Chicken has such a neutral flavor that you should pay more attention to matching your spices to your vegetables you used. The basic spices that are considered "classic" would be parsley, sage, rosemary and thyme...just as in the song. These work very well when you use the classic veggies. But when you use other vegetables, then there are some really good combinations available. For instance, if you used tomatoes then you would be making a mistake to leave out the basil. Spinach and marjoram work very well together, while tarragon and fennel make a good pair.
But don't think just about spice and herbs. If you want a really refreshing flavor, add a bit of lemon juice. Don't forget about the garlic either, as it works with almost all other ingredients. And lastly, don't be afraid to add a bit of spice. You don't need to add so much that it burns the palate; just a little will heighten all the other flavors.
Of course, I'd be remiss if I left chicken itself out of the discussion. Any cooked or raw chicken will do, but you'll find that white meat is the best in soups. Dark meat, while tastier, has a much higher fat content and tends to make a soup feel greasy. White meat for soups and pastas, dark meat for everything else is the rule that I go by.
I hope you aren't disappointed that there wasn't a recipe that you could follow to the letter in this article. The truth is I don't usually cook that way anymore. I found I made much better meals once I understood the basics of whatever meal I was making I could improvise and make improvements and substitutions based on my tastes, who I was cooking for, and what I had in stock.