I don't know if this counts as "available off the bat" but I like it if when we finish the game, we can "unlock" the gallery scenes we haven't already. Especially when its very few scenes that are locked and not worth replaying the whole game over.
I tried one game and played it for like 3 minutes (I think it was a management and turnbased combat game), wasn't a fan. I never went back since I found VN's, so I can't recommend anything.
Was Big Brother that big of a game (in this section of the internet)? I think it was one of my first, could well have been my first, but it was too confusing progress-wise that I quit and looked for other games.