Technically the original Star Wars should count since it was budgeted at around $8 million (but wound up a little over $10 million IIRC.) If memory serves, I think I read Kurtz saying somewhere that it was about as much as the studios would spend on a comedy back then.
What counts as "classic" is also a bit of a subjective concept since for people of my generation, it'd be the slightly older movies from the 70's and prior, but to someone in their teens or 20's, it'd include the movies from the 80's & 90's that I grew up with.
I wish I could rattle off some good examples, but honestly I'm not as well up on pre-70's sci-fi or horror as I'd like to be (or indeed, cinema in general!) Most of what I've seen and *like* are the fairly obvious and well known ones (War of the Worlds, Forbidden Planet, The Day the Earth Stood Still, The Thing from Another World, Invasion of the Body Snatchers etc.)
As for movies I grew up with: I have a lot of affection for 'Explorers' which seems to be obscure for anyone not of a very particular age. Aside from being a fun little adventure movie that manages to hold up surprisingly well, it also introduced me to some of the aforementioned classic sci-fi movies.