Which faction is the most interesting to play as, and what strategy do you find most engaging?

Choose Elves and focus on luck.

Luck is certainly good and important, but leadership is also worth considering. There are very useful perks there, such as: speed aura or empathy + light magic, and the Battle Mage skill itself is important.
Winged + Light Magic (mass haste, mass smite, mass stone skin) + attack + leadership (empathy or aura) + luck + logistics (quick mind) = awesome.
You can also go with: empathy + chaos + alt-druid + education + luck + attack/defense = awesome.
There are many different strategies.

I think it's not worth focusing on light-skinned races in Castle.