Cheever is known primarily for his short stories. You might try “The Five-Forty-Eight.” If you like it, you can continue with some of his other stories. If for any reason you don’t like it, it would be fair to move on and revisit him in the future. If you begin a story, I recommend you finish it, however.
Feel free to read often in your favorite genre. You do not need to finish a set of “great works” before enjoying books of your choosing. In any case, you will find popular authors across many genres who write well. In science fiction, for example, Bradbury wrote with a distinctive literary flair. Actually, if you mention your favorite genre, we might be able to recommend some quality authors for you.