I love romance novels, so I like the idea of a choose-your-own-adventure story and different routes. Plus, reading books/consuming media from different countries interests me in terms of how culture/humor/values translates into the story.
I usually only do ones I like, unless it's a mystery or I'm required to do one route to unlock another... Though sometimes I will be interested in characters I wasn't initially attracted toward, and I will end up playing their route!
I dislike love triangles in general, so this trope is a no-go for me. Unless it's in a game like Tokimeki with heavier gameplay mechanics. I don't like when women are pitted against each other, and the LI almost never reacts well...
I actually loved Tokimeki/Love Revo's stat raising. I felt like I could just idly play while doing other things. That being said I am not a fan of puzzles/minigames...
It depends! I usually have 2-3 LIs I really am excited about, and will look at route order to see which one to play first between those. However, for Collar X Malice I did use route order because it was a mystery.