Waiting for Imperialism? I got the achievement in 1580 and wouldn't wanted to wait longer.
I would definetely go with religious. 3 missionaries (base, religious, defender of the faith) are more than enough. Why do you want to stuck with 0 tolerance if you can have 10? (3 base, 2 coptic, 2 religious, and I frequently had an event which gave another 3)
I wasn't able to expand in my run after 20 years because of a blobbed Adal/Mamluks alliance which blocked me entirely. Jumped on them when they were in a war against Hedschas and was able to break Adal before the Mamluks came. After that, I had insane luck with the event that gives you a 100 tradition general. Without that, I wouldn't be able to peace out the Ottomans when they jumped on me with just giving them Sinai and 3 other provinces. Allying Spain and Austria prevented further wars, but they were not strong enough to really help. Then I just sat there and waited, conquered South India and Malacca, and when the Ottomans were in the 30 years war, got hit by internal trouble and Syria and Epirus getting all greek culture provinces broke free, it was easy.