Although I'm a PC user, I use only 5 or 6 mods for Morrowind and even these are minor, so I think you can immerse yourself into Morrowind no matter if you have access to mods or not.
My current character started as a priest, a monk / priest actually, although right now he's occupied with other things, so he put IC quests on hold, perhaps for good. From what I've seen, the quests are interesting and diverse, some of them don't involve any violence at all, but even if we put quests aside, roleplaying a priest can be interesting; your character could visit various Imperial shrines on Vvardenfell, pay his respects by either leaving some gold at the shrines and some flowers or any other appropriate artifact. He could also help poor people which are in abundance all over the island, take care of dead people, there are many corpses on the island and someone should bury them after all. Since 'dispose of corpse' option is available, that could be interpreted as 'a burial' and he could also place a petal or personal belongings of the dead on these 'graves', to mark and honor them.
These are just a few ideas but I suggest building a backstory and some personality before starting, set basic morale, priorities, traits etc...it's not necessarily but it may help, I usually do it, not in details but just to have a basic personality to start with, so it doesn't feel like a walking shell but like a living, breathing individual. The true personality and story will unfold as you progress through the game and that's when you'll really get to know your character.
Good luck!