Sounds like you're interested in sci-fi movies with a deeper philosophical story to tell. For that reason, definitely watch Tarkovsky's Solaris. From what I understand, it bears literally no resemblance to the 'remake'.

I know Stalker often gets put in the sci-fi category, but I'm not sure it will satisfy someone setting out with typical expectations of the genre. It's a great film though, and the dream sequences are peerless in film history.

Tarkovsky's films very much run against the grain of Western cinema - they are often experimentally slow, to offer an extended exploration of a philosophical or aesthetic idea. They're extremely strange and unique movies. I would say, essential viewing, when you have the time and mindset to be taken on a journey that at times will feel painful. Though, I think that's Tarkovsky's intent to some degree.