Steins;Gate starts off so slow. Like, I cannot emphasize this enough. You will be reading for half a dozen hours or more before anything happens. It's a good game but I would really not recommend it for people who have no experience with visual novels. You could watch the entire anime adapation before the story starts in earnest in the VN.
999 and Danganronpa are both good but Danganronpa is a lot cheesier I think. 999 would be my recommendation.
This!!!!!!!!
Yes, the story in Steins;Gate is amazing, but that game takes AT LEAST 8 hours to get good. It's worth it, but as an entry point a VN with a bit of gameplay will serve better.
DanganRonpa games are fun, but 999 is a true masterpiece and showcases what VNs do right much better in my opinion.
Another downside to Steins;Gate is that after the first game, the series is half told in untranslated Light Novels. I just finished Steins;Gate 0, and there was just random stuff happening at the end, that apparently only gets fully explained in those books. That's a heavy downside for me.
Also, someone mentioned The House in Fata Morgana, and this is still my favourite VN of all times. Please consider this, it's an absolutely wonderful experience. (Try the ones you like first.)
Lastly, I think you would REALLY like "
To the Moon". I have actually been advocating "To the Moon" as the entry drug to Visual Novels for years. I mean, I guess TellTale games work too...
To the Moon looks like a 16bit SNES RPG but actually tells the story of two scientists that implant fake memories into dying people's minds to fulfill their last wishes.
If you're into SciFi and interesting story, this is a good, relatively short peak into what VNs can achieve.