Here is my experience regarding this topic specifically puppeting, especially early on in pre-Renaissance era. Stepping back a bit to bring it into context, Standard game, Standard speed, King difficulty, playing as Germany (BNW), on Continents. Early war with Austria just to capture her settler as I needed a worker in Ancient Era. Shortly after in Classical Era, Austria proposed peace and offered their second city in the deal. If the city was bad I would have decline and continue with the early war which is painful but that is for another discussion. The second city, 4 Population, only has one-ring (two farmland, three marsh, and one deer) and has not expanded cultural borders. I can see on second-ring are better with at least one unique lux I don't have. Given that I decided to accept the peace deal along with the puppet city.
Looking back not sure if this was a good idea and here is why. The puppet city is far from my capital for starters. What is worst it has zero buildings which means zero culture so the puppet does not expand its borders. It builds a market, library, then monument. By now, game is in Medieval Era and I am approaching to take the capital city Austria, which has that unique lux that the puppet city has. I could not annex, even now, because of lack of happiness and to build a courthouse would take too long.