Interesting question. I’ve been poking around to see what I could find on contemporary reviews and comments.
The quick summary is that the book as treated as a major publication by a up-and-coming writer. It was reviewed favorably in the New York Times. Orville Prescott wrote: Fahrenheit is “frightening in its implications… Mr. Bradbury’s account of this insane world, which bears many alarming resemblances to our own, is fascinating.”
Even small papers like the Delta Democrat-Times of Greenville, MS reviewed it. “Bradbury often makes one think, occasionally annoys with what appears to be an exaggeration of probability, and always interests.”
Kingsley Amis devotes several pages to it in New Maps of Hell, the first critical mainstream book on sf as an art form, so it was already a classic by the late 50s, when Amis was writing.
Just the fact that it was published in hardback was significant for a story that has first appeared (as “The Fireman”) in Galaxy magazine in 1951. They padded the first edition out to fuller length by the addition of two short stories left out of later editions.
And the special edition of 200 signed, numbered copies in asbestos is something that is done only when a publisher wants to make a nationwide publicity splash. That alone makes it stand out from any other sf book published at the time. Or ever.
That’s probably the single most valuable book in modern sf. Here’s the copy that L. W. Currey, one of the top two or three dealers in sf books, has for sale. It’s $17,500. Barry R. Levin, Currey’s only true rival, has a slightly worse condition copy for slightly more.
The story has flaws that everyone recognizes, and it is usually called a lesser novel than 1984, but it was a major publication from the very beginning. Certainly, it got much more attention than that other book published around the same time, The Fellowship of the Ring, by some English professor.