"Silent Hill is a game I've been meaning to get into, so that's a good one. Would it be better to start with the first or go for the 2nd (since I know that the 2nd is kind of the god of horror games)?"
Eh? No. Something about not being able to proceed in any Pyramid Head scene without doing something senseless "shooting him with all your bullets," "Sprinting down a hallway perfectly lest Pyramid stabs your girlfriend whom then gets stabbed anyway (using controls that don't exist in other games)"
Or any other instances of nonsense such as "Yes, keep sticking your hand in things for prizes," "You have to shoot the fat human guy 30 times with a hunting rifle before he gets shot to death," and "Her dad will keep groping you in her room until you master the weird running controls" would probably be put-offs.
Silent Hill 3 is a lot more macabre, but it suffers in the control and puzzle departments (DO NOT exceed the "normal" riddle difficulty.) The Borley(?) Haunted Mansion 2/3 of the way through features another "run down a twisty hallway fast lest you lose" which may or may not be off-putting. She might appreciate the theme park and the Silent Hill takes on the mall, hospital, and church.. if you didn't say she was timid.. Why are you trying to subject her to Silent Hill?
She might like Okami. Okami is very artsy and the controls are easy. Ico & Shadow of Colossus might also be something.
She could probably get into anything Shin Megami Tensei. Shin Megami Tensei Nocturne, Persona 3, and Persona 4 especially. Nocturne (Lucifer's Call in Europe) is the best in the series (no voice acting though.)
Since they're RPGs, the difficulty is less in controls and more in planning ahead. The Shin Megami Tensei games aren't sissy, but I imagine a game that requires mental as opposed to button-mashing skills would allow her to really get engrossed in it. Most of the series has difficulties to pick from if she finds one too stressful.
They also have horror elements. They're not blatant enough to frighten anyone, but they're interesting. The Labrinth of Amala's red blood-filled walls, the eyes that stare at you there, the misty dream world in an office building where people are being tortured, the murder mysteries in all of the Persona games, confronting Fallen Angels that are panicking because they can no longer talk to God in Digital Devil Saga, Confronting the psychological trauma each character has in Persona 4, etc.
Kids that are just getting into games tend to get more satisfaction from Turn-based RPGs (Pokemon, Dragon Quest, Final Fantasy) than action games. It's because, while they can be challenging, the challenge is in their control. Whether through planning ahead, leveling up a bunch, or finding a better item etc. This is probably why most MMOs are RPGs. Everyone can get into them and a single game can last a long time.
