What a disaster. I didn't realize that people who don't play games basically can't use dual analog controllers.
I can't believe people are actually suggesting Dark Souls, anyone who's truly new at games will be overwhelmed and quickly give up.
If you want to get someone into games who's never held a controller before should at the very first learn how to use a controller. What you need is a game where you can move around without having to think about things such as timing.
Portal is the perfect game for an absolute beginner. From the start of the game you can just move around learning the controls, which, apart from the dual analog movement of any first person game, are extremely simple. There's almost no timing and no punishment involved in the whole game, so you won't ever get frustrated. The rules of the game are very simple and are laid out at the start. And besides all that, it's a great short game so anyone can finish it.
After that it's Skyrim; first on an easy difficulty and, as the player gets more experienced, he can turn up the difficulty up to a medium setting. The game is long enough that the player will get enough experience to make this possible. Skyrim is very simple and repetitive, and it can easily last over 100 hours so a newbie will get plenty of experience. It has huge breadth but I find it's not really deep, which is perfect for someone who wants to learn a lot. And after Skyrim I think you can play anything (except Dark Souls, please not Dark Souls).
I agree. My girlfriend has over the years started to do plays some games, and she hadn't really played a lot of games at all before that. 3D games in general were too hard to start with, as controlling them just isn't intuitive if you've never done it before. What really worked though, were the latest installments of Rayman. It's clear what you have to do, it increases its difficulty nicely, the controls are easy to understand, it controls very well, it's a great environment to be in (both visually and audibly), it doesn't provide too many options so that it becomes overwhelming, there is no time pressure. Good platformers like these have shown to work well for her.
Once you make the switch to 3D, then Portal 1 and 2 are indeed great suggestions, although perhaps not to completion. Again there is no time pressure, there aren't too many options, you can explore at your own pace, etc. I would say more childlike, easy-to-explore 3D games, such as Spyro, Mini Ninjas, etc. are good starting points as well. No pressure, lots of exploring on your own pace, easy to understand controls, etc.
As a follow up to those, I agree that Skyrim could be a good suggestion, although it's of course introducing a whole new complication on top of the actual gameplay, which is getting to understand relatively complex RPG mechanics. I would perhaps sooner go for Bulletstorm, Darksiders, Bioshock Infinite, Batman Arkham Asylum, Assassin's Creed 2, those type of games.
Burnout 3 was something she understood almost instantly, so perhaps racing games are a good way to start getting a feel for 3D environments. Furthermore, I also think games like THPS 2 and 3 could work at this stage to improve their responsiveness.
Dark Souls would be at the very end of my suggestion list. Although I have played games all my life (though not too many deep RPGs), Dark Souls was too complex and explained far too little for me to truly get a grasp for the entire game, despite the fantastic and addictive gameplay. Either exploring for many additional hours or having to relatively often look online for suggestions and explanations are fun if you're into it, but absolutely not for newcomers. On top of that, the fights - although fair - are obviously very hard master with many, many inevitable deaths followed by having to play the entire part again and again and again, which can easily demotivate them. You need visible progress to stay motivated, and getting real progress in Dark Souls requires a lot of effort and patience, especially from newcomers. If they even get as far, the Taurus Demon (or alternatively Havel) will get most of them to give up.
Obviously, there are many genres of games (many of which not yet mentioned). I believe taking into consideration which type of games the newcomer is interested in should be a very important part of the suggestion with which games to start. Then, if possible, start with 2D installments and focus on simple and responsive controls, not too many options, no pressure, etc., so that they can explore on their own terms. After that, gradually increase complexity in one direction or another to provide more challenging tasks. That's how real learning happens. You can then go deeper into that direction, or broaden their horizon by providing a different type of game.
In addition, watching other people play helps quite a bit as well. I'm currently replaying Dark Souls and explaining my girlfriend when she's watching what I am doing and why. As long as I don't go into too many Dark Souls-specific aspects, this will teach her some of the general rules of RPGs/3D adventure games, making it easier to understand mechanics in general.