The novel that changed my understanding of what the first-person narrator can do is Kazuo Ishiguro's The Unconsoled, which is narrated by a pianist named Ryder who is arriving in a central European city to give a concert. Ryder keeps forgetting important things. He is introduced to people he should know and doesn't recognize them. He accepts impossible spatial information without registering that it's impossible.

The effect is disorienting in a way that gradually becomes clear: Ryder is not an unreliable narrator in the usual sense. The novel is structured like a dream — the logic is internally consistent but not realistic logic. Ryder is moving through obligation and performance anxiety and disconnection from his own life, and the surrealism is the accurate representation of that state.

I don't recommend it as a first Ishiguro. I recommend it as a third or fourth, after you've developed enough trust in his method to let the disorientation work.