I loved Mark Twain's
A Connecticut Yankee in King Arthur's Court when I was ten-ish: probably where I got my fetish for time bending and alternate history. A little later I acquired
Born into Light by Paul Samuel Jacobs, about the appearance of uncanny feral children around the world, and a slim anthology called
Out of This World, which introduced me to Vonnegut, Asimov, LeGuin and Bradbury, as well as classic stories like To Serve Man, Betelgeuse Bridge, and A Bowl of Biskies Makes a Growing Boy.
I'm pretty sure all of these were scored from
RIF.
EDIT: and Fritz Leiber! He had a great story in there, A Bad Day for Sales, about a robot salesman roaming nuclear winter in search of a prospect, like Wall-E without the happy ending.