I have a signed copy of the first paperback edition... it's one of the treasures of my collection, too (though I envy your hardback edition, Ian).
Wow! What a fabulous edition to have... and you envy
me?
Must confess, when I first saw Allegra's request for advice, I dithered because I didn't know quite
what to recommend:
Fahrenheit 451 itself would be a great way to start reading Bradbury, but then there's the oft-mentioned:
Martian Chronicles/The Silver Locusts -- such a wonderfully alegorical collection of stories, seemingly almost pastoral at one level, but passing comment on trends in American society at another...
The Illustrated Man -- a really neat way of linking diverse stories, with each springing from different tattoos on a carnival man covered with them, the tales given a common thread by being told as stories within a story...
The Golden Apples of the Sun -- which, apart from anything else, features the wonderful "The Sound of Thunder" -- one of the best time-travel stories ever (See how many times it picks up mention in the current '5 best time travel stories' thread over in the SF loungs, from myself, Neal Asher and others)...
Something Wicked This Way Comes -- A tale set around a sinister carnival at Halloween, which manages to be both terrifying and enchanting at the same time (and it's recently been reissued in the UK as part of Gollancz's Fantasy Masterworks series)...
And I haven't even mentioned
The Machinaries of Joy, Dandelion Wine or
I Sing the Body Electric.
To be honest, any of the above would be a great way to start reading Bradbury. The important thing is, don't miss out by not reading him at all... and if you could throw in a bit of Theodore Sturgeon, Fritz Leiber and Jack Vance along the way, then you'd be really cooking!