Playing noble ang going for a domination of asia seems to be everybody's choice. But, in fact, Japan like the English has the great advantage of being isolated. Insularity is the key, even if Korea and Thailand are rich lands. For some reasons, I don't advice settling on the continent.
1- It's quite dangerous to colonize Korea. Whatever you do, China and Mongolia are going to exceed you in term of production and by the way you send a settler there, China has already put a city here, a very good one and trust me, it is not good to become the target of mongolia once Gengis has keshliks
2- See maintenance cost strategy. China would be I think your best ally. You need to let Qin Shi settle everywhere on the continent but not in the islands. Doing so, China is going to face tremedous maintenance cost and won't be a menace for you to grab all the lucrative southern islands. Same thing for India.
3- See military strategy. As I usually do with Elizabeth, I use continental powers like an army for me. China should protect you and in return, you need I think to grant Qin Shi for his protection. If you want to conqueer him, wait for tanks, Samurai won't last against Chu ko nu....but anyway, I think it's a better idea to see China as a great wall for Japan.
4- See Key ressources. Your main rival is situated on the other side of the map: England, the forever tech leader. You can compensate Elizabeth's ridiculous advantages (philosophical/financial upon islands including stone!) by getting calendar's ressources and think about corporations, mainly sid's sushi, ethanol and civ jewelers. You need Oil and Uranium. Oil can be found on the Borneo's shores and Uranium is waiting for you in Australia. So, as you see, there's no need for you to settle on the continent. You'll be able to trade for missing ressources such as deer, cow, sheep and obviously England is your best trade partner, while opening trade routes with chinese giant cities (think about the GLH) is a good way to make a ton of money (intercontinental routes, which is not the case of you colonize the continent). If you want horses or Ivory, I think that both Catherine and Mansa would exchange them against some of your calendar's ressources.
So the key is: Settle the islands (don't forget Taiwan!) and until you colonize the whole southern Asia, do not intend a war, that will be to expansive. Once done, you will be able to start and finance any war. It's usually a good idea to do so in America.
On this map early rush are good only for Germans, Romans and Greeks
Sorry for my english