Chinese is of course the oldest. Japanese is the youngest.
The Japanese in its earlier days was wanting what China and Korea had in the way of arts, science, and construction. They offered land and gold to any who would come and teach. Several came and taught their specialties. They were instead killed, rather than paid, after the Japanese learned all they had to offer. What they learned they changed or improved on it an made it Japanese giving no credit to the others. I have lived in Korea, Japan, Taiwan, Thailand, and Cambodia.
The old ways of China are without a doubt the best. But because of the teachings of Confucius, (Kung Fu Tze), it became a static society and began the long slide into what is now modern China. The Japan is a country of great beauty and wonderful people.
I enjoy the foods from all the Asian countries, but I like Korean the best. I think Korean is the easiest language to learn, that is because of the way they write. They have a modern method called Hangul it is a phonetic alphabet and can be learned in two weeks studding about 20 minutes a day. The Japanese and Korean still use a writing method using Chinese characters. To be considered barley fluent, you will need to learn about 40,000 characters for all three countries.
I can not pick one over the other, I loved them all. I would suggest you consider what you will do with the language you will learn. If it is for study or for possible employment. Then either Korean, Japanese or Chinese. Chinese has three main dialects while Japan and Korea, just one each. I have feebly attempted all three, I am not very good at any. The Thai was my strongest, I could speak, read and write in Thai. I got so good at one point I could tell a joke in Thai. I have not used it since I left Thailand in 1975. In my travels I found if you try and speak the language, learn and keep the local customs, most will try and help you. I never had any problems traveling through Asia. It was only when getting shot at in SE Asia that I had problems. You can go on-line to the consulates and get a ton of information. I have used several different study courses and the easiest was Rosette Stone. Its expensive , but its also in the public library. Which ever you choose, good luck and I know it will make you a better person for trying to understand others. Don't look at it as being a "Foreign language" Its just another way to say the same thing differently.
I bid you peace.
Shalom