I'm a bit suprised by Expansion (or did you mean Exploration?) as a choice. Really America isn't going to bring you enough money in the early game to make a difference. On the other hand, I used vassals as well as direct coring to expand really quickly in the beginning. For example, I had Yeren as a vassal with 90% of the Manchu culture lands while I conquered all Altaïc lands directly. Other potential vassals are Chagatai, Kazakhstan, Afghanistan/Persia. Influence will help you greatly annexing those faster or keeping them in line if you're not annexing them immediatly (Persia is a great march to have for example).
After influence, I picked Humanism, which is great to completely negate revolts in your lands (I went yellow shamanism). Also a couple more accepted culture will allow you to accept Chinese ones in the long term (to avoid the cultural disaster once you get Emperor of China) as well as Manchus and Buryats. I'll be keeping those accepted all game long.
Then, I found that Administrative is a great choice. You should rush the first two ideas for reduced coring costs. Then, you slowly advance in the group, and I found that the Mercs ideas are really useful because I need to use Mercs to fight so many wars: China, India, Persia, Russia. Also, Age of Reformation doesn't have a lot of useful splendor bonuses, but the +5% discipline for mercs is a good one.
Finally, I'm not convinced you should rush to get rid of the Horde government. I still have it in 1600 and it helped me winning a 1v1 war against Russia, who had more troops and MP than me. But with the Horde CB, horde bonus and carefully picking battles in the steppes around Astraskhan, I was able to get a good peace deal: cutting them off Siberia, the gold mine in Bashkiria and a first foray in the Crimea region for the Great Khan achievement.
Next war against Ming is going to be the "5th war of Mandate of Heaven" and this time, I'll take the title of Emperor of China and form Yuan. No need to reform the government with the Yuan decision now.