Here are some fun achievements runs.
Of course you have the standard Basileus run, I spent my first 100 hours learning the game by trying and failing many times by going after this achievement until I got it. There is something so satisfying about throwing a wrench in the Ottomans plans right at the start, and religious ideas are actually very powerful for Byzantium.
The Re-reconquista is a bit harder, but also satisfying, and it lets you form a fairly powerful nation. Try an unlikely candidate if you really want to cut your teeth though ( I keep failing it as Mzab).
Mewar never changes is a great achievement to go for if you are new to playing in India. Mewar had great military ideas, and can form Rajaputan before forming Bharat. You can also get an achievement for having a certain number of rajaput regiments.
Austria has three achievements, with AEiOU requiring you to finish the mission tree. Austria is also likely the best candidate for One Faith.
Want to play a run where you will have exclaves and PU unions all over the place? Try good king Rene. Province can have an explosive start which starts with a high relations Papal States giving you your core back, and can end with forming Jeresulem ( you must form it before the age of absolutism).
That's all I can think of now, I might add more later.
