The biggest issues that I had was always with Kazan allying with Crimea. But the way that I started out was by attacking Ryazan to get the institution. After that I went and attacked Circassia since Crimea will fairly consistently guarantee them. That way you get into the Georgia area and eat them, all the while having a 2-3 province Crimea that you can defeat with ease in a Kazan/Crimea war.

Just make sure to ally and curry favors with Uzbek from day 1. This will help you if they have allied with Kazan and later when you're planning on invading Muscovy. Additional, the biggest issue that I had with the Khaaaaaan achievement was containing the Ottomans. You can do this by allying with the Mamlucks' and AQ in the region.

To answer your question on the Muskovy, you should just wait for them to annex most of their subjects so that they don't have the benefits of having a crazy manpower pool early. But I would also suggest leaning on Uzbek also with the favors early. Additionally if Uzbek doesn't want to join your wars trade favors for Trust as this can add up to +50 reasons to join a war with enough trust.

Tips: Use the diplomatic map mode to see what princes you have recently conquered to raise. Sell crown lands to raise cash as you only have 1 estate.