I'm definitely a bit of a newbie when it comes to VNs, but here're my thoughts:
Doki Doki Literature Club - Great VN to start off with if you don't mind some horror. It's especially effective if you've played a number of VNs already
YOU and ME and HER - Where DDLC is more suited for a general (western) audience, YOU and ME and HER leans more heavily into being a visual novel. It's a pretty good time.
STEINS;GATE - The absolute masterpiece that everyone recommends, and is one of my all-time favourite sci-fi stories featuring time travel and the realistic ramifications of such an ability. If you've already watched the anime, there's lots of content it glossed over so as to find in a 25 episode series, such as the entirety of Chapter 7, and an optional section of Chapter 9.
STEINS;GATE 0 - Sequel* (not actually a sequel, but takes place during the true end of STEINS;GATE) to STEINS;GATE, and is one I've been making my way through. It's also a great time, and explores some pretty unique ideas for its time.
Phoenix Wright: Ace Attorney Trilogy - The classic DS game remastered to a PC release, its humour still holds up to this day, and it's a really nice balance of visual novel style text after text, and actual gameplay mechanics. I would encourage the use of a guide if you struggle in some court cases, as it's not always obvious what you need to be doing.
the Danganronpa series. I found it surprisingly good and I even went and watched the tv series that bridges the second and third games. The plot starts off the same way in each game where a group of kids find themselves kidnapped with no recollection of how they arrived in their current situation and are forced to kill each other to survive the situation as they scramble to uncover the truth before they’re killed. Each VN can be played as a stand alone entry but it’s far more enjoyable to play them successively because the overarching story connecting them is woven into each. There are no branching paths in this game but it’s straight up a good story.
the Ai: The Somnium Files series does have a branching path structure and is designed to pickup very easily from any scene in the tree to come back and explore later. Indeed you are invited to explore the timelines Because you’ll be prevented from progressing too far in one timeline if you don’t know the relevant information you need to continue that is explored in another path. I haven’t played the sequel titled The Nirvana Initiative but it was recently on sale on steam for a pittance so I had to pick it up.