hello and welcome.
i suggest you try the muv luv series (muv luv extra , unlimited and muv luv alternative) , ever17 , clannad , fate/stay night , sharin no kuni himawari no shoujo , saya no uta (if you dont mind gore) .......and theres a few more that i cant recall right now. All of these are heavy story driven VNs , there are H-scenes in all of them (except ever17) , but they pretty much all have a heavy plot (muv luv extra is a slice of life comedy , but you'll know what i mean once you start with Alternative) and are some of my personal favorites.
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