You’re asking the wrong questions. Where do you get the soup that you love and what do you love about it? There are literally 3,679,264,916 chicken soup recipes – many simple, and most of them (at least in their creators’ eyes) really good. There are many dozens available online.
There can be a lot of variation in chicken soup recipes (noodles, rice, to cream or not to cream, vegetable choices, herbs, etc.), but the heart of any chicken soup worth its salt is a real chicken stock – not a bouillon cube, not a can of broth – a real homemade chicken stock.
Make one by putting 5 pounds or so of chicken pieces in a stock pot with enough cold water to cover. Bring it to a boil, reduce the heat and simmer it. Skim it periodically until no impurities remain, a half-hour or so. Then add a coarsely chopped onion, a carrot and a celery stick, as well as a bouquet garni (a bay leaf, some parsley sprigs and a little fresh or a teaspoon of dried thyme tied up in a bit of cheesecloth). Simmer it all for three hours, adding enough water to keep everything below the surface. Strain it into a clean pot, let it cool, then refrigerate it. Remove the fat that congeals on the surface before using the stock.
Now with this stock, you should be able to make the chicken soup of your dreams, whether that includes carrots or noodles or whatever.