Have always used the chicken carcase for making stock, did this the other day but used far less water than usual probably about 15 fluid oz. Simmered carcase, skin etc with a bay leaf and some thyme for about 35 mins. I do mean simmered - no boiling. Strained and left to chill. Scraped off all fat. Added some spring onions, black pepper, salt and a bit more thyme (fresh-but dried will do). Warmed very gently and added a large tablespoon of quark. Al had half with me so it did not last long.
Cock-a-leekie - mainly chicken, onions and leeks is a simple one. If doing for family too add potatoes to theirs. Can add garlic too.
A lot of herbs go nicely with chicken, sage, parsley, tarragon, but my favourite is thyme.