Technically, my first VN was Phoenix Wright: Ace Attorney. I loved it. It is still one of (as in, second or first place) my favorite video game franchises, period.
The thing is, I definitely didn't see it as a VN when I was playing it. I saw it as more of a Japanese take on the "Adventure Game" genre, with all the pixel hunting and moving from location to location. I still see it as more of an Adventure game than a VN, but hey, if it's under the VN label too, it certainly doesn't hurt me in any way.
The first time I consciously played a VN was Katawa Shoujo.
And my god, that game.
I happen to be a burn victim with severe scarring, and the first route I played (entirely by chance) was Hanako's route,and it blew me away. I have some very similar social anxiety problems (though not as severe) and deal with the self-consciousness that comes with having burn scars on a daily basis. I'm lucky in that my scarring is restricted to my legs, so I can cover it up, but I still felt an extremely close connection to Hanako. I feel like they tackled the issues someone with severe scarring goes through fairly well.
I actually wrote an in-depth blog post about my personal reaction to the game as a burn victim on another site (along with the details of my accident), maybe I'll link to it on Fuwanovel sometime. That time is not now, though. Not quite ready yet, I want to be a bit more established here before I go spilling my guts in such a transparent way.
Needless to say, any reservations I had about enjoying the VN genre were totally gone after that experience, and I got a lot more into it. Finding out that the Ace Attorney games are also considered Visual Novels just cemented my interest even further.