The Sword of Islam and Legacy of Rome are a must if you're looking to play the respective states later. Otherwise, they're not needed. However, Legacy of Rome is needed in order to unlock retinues, which are very useful as a private standing army. You can do without them, but it will certainly limit your options a little.
For ahistorical lulz, you can also look at Sunset Invasion to trigger the Aztec horde on Western Europe at around 1300s thereabouts. (Similar to how the Mongols will appear in the 13th century.)
I'd also recommend the songs DLC, if only because I love Waldersoft's works.