Hi Donny,
I'd strongly recommend that you (and everyone) download and install this patch:
https://www.mediafire.com/file/8bbzq...0Buff%20Fix.7z it addresses most of the bugs that are apparent as well as some balancing.
The 3 factions that have the most difficult starts arguably are:
The Ghaznavids - historically they lasted only 10 years after the start date, prevouisly they were one of the great powers but a host of bad decisions has found them at war with the Ghorids in the west who have already taken their core provinces, the Rajuputs in the East who have in the past long suffered from Ghanzi raids and the Malikate of Sindh to the south. They are the wrong religion for their cities, their armies are stretched thin and the troops readily available are sub-par indian levies. If you can overcome the initial difficult position you have the foundations of a strong economy, elephants to recruit and a chance to fight the mongols earlier than most.
The Volga Bulgars - They're on the northern most part of the step, previously they were one one of the great trade hubs of the world but following years of Rus aggression their homelands have been devastated. Surrounded by enemies on the steppes with enemies that arguably can produce better troops then they can at a faster pace.
Then I'd say its a tie between
The Bavandids and
The Kievan Principality.
The European favorites of ERE, Armenia, KOJ, Georgia and Makuria all work as good late game opponents to the mongols. Other options I'd recommend are either of the Rus factions, any of the three atabeg factions or three factions in arabia for a very different playstyle.
Each faction may most of their faction specific units in every region of the map. However, to do so you must construct faction specific recruitment buildings that can be expensive and time consuming to be built at higher levels to offset the loss of BC's traditional AOR.