Hobo Elf
Arcane
Arguable. BG1's story is generic and boring and the companions aren't half as developed as in the sequel. I guess it can count as half a storyfag game, but the main focus is on questing (fetch and kill quests) and crawling through hordes of bandits. I might be biased though because I don't like BG1 that much, it just feels too generic to me so I always ignored the story.
I actually like the story in BG1. Well, at least what it was trying to do anyway. The Bhaalspawn stuff is boring wank, but I really enjoyed Sarevok as a villain. Instead of being a generic fantasy thug who just brutes his way through with strength he used politics and the economy to cuck the Sword Coast, i.e flooded the market with shit iron that is frail and breaks apart randomly, and then maneuvering himself into a position of power by appearing as the only guy who has all the man power and connections to battle the iron shortage and increasing bandit activity. This is great because it's also tied into the gameplay where non-magical weapons will break eventually. Usually the leap from Sword to Sword +1 is a significant one in D&D, but in BG1 it's extra important and feels great because now you don't have to worry about lugging extra weapons around in case they break apart.
But as you said, BG1 isn't much of a storyfag game. It's more about going on little, random D&D adventures. The plot was mostly just there in the background until the very end, and its purpose was to serve the gameplay, rather than forcing the gameplay to serve the plot.