The secret of good soup is in the stock. If your stock is good and full of flavour, you can add mostly anything by way of vegetables/meat and it will taste great. I've seen beuautifully presented soup that did not taste good because the basic stock wasn't good in the first place.
If you make your own stock out of the bones from a roast chicken, you can't go wrong. Just break the carcase up with your hands, place in a large saucepan and fill with water so that the bones are covered. Simmer gently for a couple of hours. Then strain through a sieve and allow to cool. When cool, cover the stock and place it in the fridge overnight. The fat will have solidified and you can just pick it off (chicken fat is actually great for making roast potatoes, or generally for frying!).
Some people like to add onion/carrots etc. to the stock while it's simmering but I don't see the point.