Hmmm. Considering the man has been publishing for close to 70 years....
Weeellllll... I would definitely suggest getting both
The Martian Chronicles and
The Illustrated Man, for one thing. Both are classics in their own right, and there are some interesting connections between the two as well (stories which are sometimes sequels, sometimes mirrors, of ones in the other collection).
Fahrenheit 451 is, I think, still a classic, but I don't think it is his best, myself. But I would definitely pick up
Dandelion Wine and, from an entirely different phase of his work,
The Halloween Tree (which is much more than simply a spooky tale, as it is also an evocation of childhood, the mysteries of growing, a history of the holiday, and a look at what it means to truly love a friend). I, personally, quite like the collection
I Sing the Body Electric, and find that
Long After Midnight is also a very effective collection of tales, while such things as
The Anthem Sprinters and Other Antics or
The Wonderful Ice Cream Suit and Other Plays are among the most enjoyable modern plays I've encountered; I also have a strong fondness for
The Golden Apples of the Sun; while the anthology I mentioned,
Timeless Stories for Today and Tomorrow, gives an idea of what he is like as editor... and gives a great deal of insight into his own tastes and the things which influenced him.
Ummm... not really being very much help here, am I....?