Empires overview
Permanent War
England is at permanent war against France.
The Latin Empire is at permanent war against both Byzantium and Bulgaria.
The Easy:
Byzantium - half of the Empire was lost in the fourth crusade, but they are in a position to recover, with the Latin Empire being very weak and disorganized. Once they are out of the way, the Venetians might be dealt with, and then Byzantium will again be among the great powers of Europe.
France - locked up in a conflict with the English, they are at least likely to be the winning side. Once a great prophet can be generated, the Avignon Papacy will provide the cash boost to drive the English out once and for all. The holy land provides several luxury goods if it can be held.
Turkey - the various Seljuk sultanates have long suffered from internal conflict, but with a strong leader unifying them they are in an excellent position to expand. As long as the Mongols can be kept looking the other way, they will have Anatolia all to themselves.
Spain - if they can drive the Moors out quickly, they will have Iberia to themselves, and be very safe from invasions - France is likely to be friendly. The Spanish can then expand into North Africa or Sicily at their leisure.
HRE - Have the Apostolic Palace with their own religion. Lots of land and good production, but under cultural pressure from several directions.
The Medium:
Mamluk Egypt - One of the largest and most powerful empires at the start of the scenario, they have several things going against them. They are spread out, are constantly harassed by barbarians, and are being invaded both by Mongols and the Fifth Crusade. They do at least have Mecca, and if they can overcome the initial difficulties they can become very powerful.
Mongols - The largest and most powerful empire at the start of the scenario, their economy is in terrible shape and is crashing fast. Raiding neighbors for cash could be a quick fix, but it will be some time before they can get their economy into shape to do some actual conquering.
Almohads - Face many of the same troubles as the Mamluks, but are even more spread out. North Africa does have a lot of unsettled land, and if they can use it they have excellent growth potential.
Venice - Start with an advanced government, have many strong cities and the best fleet by far, but are very spread out. Their fleet allows them to strike anywhere they want, though, and there are plenty of good targets within range.
Papal States - Start out small but have excellent culture and are able to gobble up Sicily should they choose to. Rome gives plenty of extra income.
The Slightly Difficult:
England - Winning against France might prove difficult - they are larger, stronger, and have a holy city. There is also the risk of Spain attacking you while you are busy with France.
Bulgaria - They are large but technologically backwards. The Latin Empires gives plenty of conquering options but they must think twice before going up against a more advanced power.
Hungary - Culturally pressured by Venice and likely to be invaded by both Serbia and Bulgaria, they nevertheless have some decent cities, and will be in a good position if they can recapture Dalmatia from the Venetians.
Sicily - Tend to be culturally pressured by the Papal States and the production is not the best, but they have the opportunity to expand into Tunisia.
Serbia - Start out as a one city minor, but with a very strong army. They can go any direction they choose! Bulgaria and the Latin Empire are especially tempting targets.
The Difficult:
Latin Empire - With a terrible government, poor army, and bad economy, the so-called Latin Empire is not doing well. Both Byzantium and Bulgaria are after their blood, and it will be difficult for them to survive.
Georgia - Tiny, bad cities, and liable to be invaded and burned by Mongols. There is really no easy target nearby, the best strategy might be to wait until the Mongols are occupied elsewhere and then try to steal a few cities from them.
Armenia - Tiny, terrible cities, and squashed between the Mongols, Turks, and Mamluks. The Levant might be a possible target for expansion.