Thoughts on introducing someone to video games? (Bookmark for GAs)

I would suggest you pick a few titles from different genres and look up the game trailer where they either kind of tell you the plot (ie: the lead into the story of the game) so that way she can see and choose which one drew her in the most.
As for me i was drawn into gaming from watching my younger brother play Final Fantasy VIII (VII's graphic at the time did not interest me as a non-gamer) The intro of FFVIII drew me in and i really wanted to know the story so i bugged my brother to play it whenever we were both free so i can watch the story develop, however i left home & he finished the game which got me so upset i went out & bought a brand new ps1 just so i can play to find out what happened.It was my one and only game that i played. This was when i was 16.
Life got in the way and wasn't until i met with my husband that i started to get interested back into games from just watching him play and eventually he got me to join him in FPS & action games, something i never thought possible as i thought those genres were just senseless violence with no strong plot so didn't know how it could even be enjoyable til he proved me wrong. Thanks to this, our kids grew up watching us game and now we have a great team for most MP games ;)
Everyone is different but you know her best, so trust your instincts or just ask her preference ;)

Why not start with something simple like a puzzle game for her? Maybe Plants vs Zombies or Candy Crush?

My girlfriend liked the most Stardew Valley (strangely enough because it is pixel art I thought she won't like - I was wrong though). Other than that she's also enjoyed Life Is Strange (good for a beginner because it is slow and you don't need reflex), Banished but it is a bit too hard to keep beginner interested, RollerCoaster Tycoon (you don't have it), L.A. Noire (you don't have it), The Sims 3 (maybe on Origin?). I didn't play Vanishing of Ethan Carter but I'd guess it might be a nice choice as well :)

I wouldn't go with p&c and hidden objects games because they have these strange, often irritating puzzles... My gf didn't like them either. Portal for my gf was a big no-no (check here why). I guess you will have to try different genres and see what your friend like because she will probably like something you don't expect :P Just like I didn't expect my gf will love Stardew Valley so much :P

Going through your library, i'm gonna recommend the following:

The Walking Dead - especially if she liked the tv show or the comics
This War of Mine - if she's into social justice
Keep Talking and Nobody Explodes - great party game
World of Goo - great little puzzler

Maybe Heroes of Might & Magic III. My sister, who never played any games, played that game to death

IMO it's really hard getting other people interested in hobbies they're not already pursuing. The best you can hope IME is that by being exposed indirectly they begin developing an interest naturally.

On the plus side, there's a ton of threads like this on the Internet (and guess why, I would add :)), just mentioning it in case you need additional suggestions.

I think you should choose a story driven game that has minimal controls. I suggest Telltale games such as The Walking Dead or Tales from the Borderlands. Those are a little violent though so maybe a game such as Life Is Strange or Beyond Two Souls for console. Another idea is to have her watch you play games so she can get the grasp of the gameplay while also seeing the good story, graphics, and characters that come with a well made game.

I recently found out that my boyfriend had never played a Nintendo game in his life. I grew up with Nintendo so naturally I had him try some of my old games to share my enthusiasm. He tried Mario Kart, Super Smash Bros, and Super Mario Sunshine but all of them were way to hard for him because he wasn't used to the kind of gameplay in Nintendo games. So I know how hard it is for someone to try something new for the first time :P

From your list I recommend for her to play: The Walking Dead, Life is Strange, To The Moon, Firewatch, The Stanley Parable, Thomas is Alone, or Stardew Valley. Mostly because they are short, easy to control, addicting, or have a good story. Personally I think TWD or LIS should be first

Good luck and just remember to explain to her that vastness of video games and maybe even ask her what kind of genre she is into. For example: if she likes action movies she'll probably like action games. Or if she's a fan of comedy, then comedic games are the way to go :)

You're just going to show her stuff, which means you can show quite a selection, even if it's just at video and explanation level. I don't know her, you might know what might be appealing to her at a narrative or visual level, or just learn as you go along. You seem to have quite a few interesting things in your library that won't fall into the mindless violence niche. Even many which have violence, but would be cool to show just for the cinematic feeling, such as Bioshock Infinite (which starts totally non-violent and interesting to explore) or Mass Effect.

From your library, I'd show: Portal 2, Life is Strange, Mirror's Edge, Dwarfs!, This War of Mine, Trine, World of Goo, The Vanishing of Ethan Carter. And Bioshock Infinite and Mass Effect. And definitely show the games you put most hours into, because they're you're favourites and you can be enthusiastic about them, and hey, who doesn't like Civ 5, which is totally not a mindless violence simulator, but a really thoughtful violence simulator?

Based on the games you own I would suggest Stardew Valley or Deponia. I would really suggest any HOG or HOPA type games. If you would like a key for a HOG/HOPA I do have a few on my spare key list. They are more casual games that focus on puzzles and stories.

in your library : ibb&obb, polybridge, hexcells, portal, thomas was alone, stardew valley (just avoid the cave).
If she don't want violence, avoid any mechanics involving weapon, as I saw few people talking about Trine for example.
It's also good to swap game, to not give her the impression that it's only one thing, gaming is vast, so make sure to show, or at least tell her that it's beyond what you are going to show her that night. If you had time for only one game in this, i would say Stardew Valley, as it's the easier to progress without being stuck (don't push things, if you start a game and get blocked, it won't be good to try to tryhard, it often give a bad impression to newcomer).
Also, if you let her play, never take the controller/keybord/mouse out of her hand to show something, even to unblock her. Of course at the beginning, it's going to be difficult. You'll need patience, as she will, because she is going to do mistake, or miss stuff. But it's okay :)

I tried few years ago to make my best friend into gaming : showed her plenty game i was playing -> i was so overwhelmed that i think i scared her XD at this moment, i was playing portal, skyrim, super meat boy... I wanted her to try everything, bad plan.
Last year, i introduced my step father to gaming, as he don't like it, and thought it was too violent. I played a whole efternoon with him at Overcooked. I stayed calm all along, even if inside i was screaming at how bad he was. The afternoon ended pretty well, we had finish 2 world out of 6 :D i just needed to let him get used to a controller, and eventuallly we managed to play together. he is still bad, but less ^^

You seem to like strategy and RPGs, which are not a good choice for an introduction to videogames, as they usually have complex mechanics. From your list i would start with a narrative heavy, low interaction game. The Walking Dead or SOMA if she likes horror.
Also maybe Thomas was Alone, which is pretty simple to play and has a good story.

Thank you everyone! I did read everything even though I didn't have time to reply to the latest things. Either way, update in the op for those interested :)

I was going to suggest Never Alone, but doesn't seem like you've got that one.

If your friend likes tv series, I'd suggest to start with telltale games likewise Walking Dead and The Game of Thrones. But also Life is Strange can be a good choice. Generally speaking I think that story rich and point&click games are the best choices to introduce someone to the medium :)