There is nothing wrong with liking a fighting game for its storyline. I love BB's story (as well as Persona 4 Arena, Arcana Heart, MKXL and Guilty Gear). I am not particularly good at them either. Like you, picking mains because they are easy and/or fun is fine IMHO. I did much the same, I just happen to like the characters I picked b/c of their stories and I liked their ease of use. In fact, b/c I like the story so much, I have Izayoi, Tsubaki, and two quotes from BB tattooed on my legs and a cat named Hades Izanami :).
I mostly like to play as my favourite characters (Hazama, Ragna, Rachel, Taokaka, Lambda and Hakumen). If I had to choose a main and a sub it would be Ragna and Taokaka. I can play as any character if I want to, because I can remember most special moves and distortions which helps. My least favourite to play as would be Carl. It hasn't really changed much through all the games, but I do like to play as Naoto.