I would mildly recommend SH4. Its not that great but there ARE bits and pieces of it that are genuinely great.
I would *STRONGLY* suggest not playing Shattered Memories. I hated it, for a myriad reasons. Chief among them is that it just isn't fun to play. The psych evaluation portions are mildly interesting, and the big twist at the end was pretty novel though.
The game just fails utterly to be scary, for the puzzles to be interesting, or the chase sequences to NOT be a giant pain in the ass. When you aren't getting repeatedly gang raped by the same generic looking humanoid creatures, that comprise the ENTIRETY of the enemies, to actually be able to look at the map it pretty useless. There are MANY paths that lead you back over and around the ONE series of doors that actually takes you anywhere. Its all the fun of being a rat in a maze full of cats. Only everything is iced over, so it looks the same, and its snowing. At night.
Which sounds tense I'm sure. However when you are forced to run though the same generic snowy area for 20 minutes looking for the way out as your path keeps looping you around through identical looking doors, past identical enemies, and after finding it realize that you have to go all the way back to look at some stupid bird statue you didn't know you were going to have to recall in exacting detail...it just makes you hate yourself for buying it.
The characters are all terrible, the endings all suck, all the various changes wrought by your test choices etc. are minor. The game is also REALLY short. If not for getting lost in each chase scene, due to poor visibility, total lack of any visual cue as to which path to take, and the need to never stop running EVER, I would imagine you could beat the game under 90 minutes. Seriously, almost NOTHING happens. The last 5 minutes are the only decent part of the game.
The one reason I would recommend Shattered Memories is for the soundtrack that came with it. Its awesome.
As for horror games I WOULD recommend:
Siren: The ORIGINAL one. It has one of the creepiest soundtracks in ANY game, and apart from that the sound the shibitos make when you are sight-jacking them will really creep you out. They are also pretty loud so other people in earshot will wonder WTF you are doing. Its also really difficult, so surviving may be a problem. Which used to be the POINT of these games. The story is also really good, though weird. Really weird.
Siren Blood Curse: The remake of ^. It has a more user friendly attitude and interface. Its way easier, arguably way better looking, and the plot is a little less complicated due to there being far fewer characters. Though if anything its even weirder.
Kuon: Its made by Fromsoftware, aka the makers Dark Souls. Here is the trailer Good luck finding a copy.
Fatal Frame 1-3: The first one is the best, followed by 2, and I barely remember 3 to be honest.
Silent Hill 1 and 2: The best in the series by a WIDE margin.
Silent Hill 3: Its still a great game, but it has a few minor issues for me personally that probably don't bother other people. Most notably both endings SUCK! Anything else I had to say good or bad about it would be spoilers. Well it does have some pretty nifty weapons and enemies.
Silent Hill Origins: I really liked this game. I played it on PS2 though. One boss in particular scared the crap put of me the second time I saw it. It was the *big* one, and you will know what I mean.
Silent Hill Homecoming: Interesting plot, great graphics, AWESOME bosses, but a questionable combat system. You will either love it or hate it depending on how quickly you learn how it works. The first enemy in the game killed be repeatedly, but eventually I got really good at it. Then I trying playing it again recently and I had no idea how to NOT get my ass handed to me by the same enemy. I quit playing it in shame.
Silent Hill Downpour: AWESOME game! I loved it, almost start to finish. I say almost because while I really liked a few of the endings, the others are complete shit. One in particular, let's call it the one of the bad endings, makes ZERO sense. It ignores or contradicts pretty much everything that happened in the game. One SIDEQUEST, involving a heart is easily one of the tensest sections I've played in a horror game. There are many sidequests, and all of them are pretty sweet. The enemies are a little meh for the most part. Other than that I highly recommend it.
Koudelka: Its...different. Its a horror themed RPG with a frankly bizarre battle system. Basically you send out Edward as your designated meat shield which prevents enemies from getting at your other 2 character that use magic. Edward is best left unarmed to raise his unarmed skill which in turn helps you when you put a powerful and very breakable weapon in his hands for bosses. If you want to play a game with some of the most gruesome and twisted Lovecraftian horrors attacking you in a creepy monastery then play this game. Its sequels are straight up jrpgs and a bit more lighthearted. Koudelka is straight up depressing and at times actually scary.
Perfect "Twin Peaks" game (though they were also inspired by early Suda51 "Flower, Sun, and Rain" adventure game)