Here are the 3 games I would recommend.
1. Gregory Horror Show
Based on the animation of the same name, Gregory Horror Show was a rather surreal title starring block-head characters. It was a survival horror-style adventure set in a strange hotel run by a anthropomorphic mouse, and inhabited by guests who carry the souls of the dead.
Your goal was to collect these souls and return them to Death, but the guests didn't part with their soul bottles easily, and after you collected a soul, that guests turned hostile, roaming the hotel looking for you. More guests check in as you progressed, opening up more of the hotel, and in order to succeed later on, stealth needed to be used to avoid enemies.
It was a refreshingly different take on survival horror, and one that not enough people discovered. Shame.
2. Mister Mosquito
One of the strangest ideas for a game you'll see, Mister Mosquito placed you in the role of a cartoon mosquito who has to suck the blood of various members of a family as they went about their daily lives.
Sucking blood isn't as simple as it sounds, though, and you had to find the right spot on the body that'll let you go unnoticed, and if your target started to become aware, you needed to retreat, lest you be squashed into mush.
With typically Japanese style, and some surprisingly well-handled gameplay, Mister Mosquito is a title you should check out.
3. Rez
Rez is one of those classic games that always finds its way onto lists like these, as well as best game ever lists, but at the same time it's also a game that many people have either never heard of, or simply dismissed.
A music shooter, Rez is a trip for the eyes and the ears. It's an on rails shooter that ties the onscreen action and your success to the music. As you fight, you add music and sound effects to the soundtrack, and your onscreen avatar transforms. Everything in the game reacts to the beat of the music, and the Panzer Dragoon-style controls and impressive bosses all make for a short, but unforgettable shooting experience.
It's a game that's often used in the argument of games being art, and it's one of the most stylish and addictive shooters around.