Out of this collection of short stories by John Cheever, which ones would you recommend reading?

My suggestion? Get started!
This is a remarkably strong collection, and you might find yourself reading more than the assigned 10.

Cheever was a really great short story writer. Start with The Swimmer. It’s guaranteed to get you into his writing and make you eager to read the other nine stories of your assignment. The Swimmer was later made into a film starring Burt Lancaster, a favorite at old underground film festivals. You might take five minutes to read the Wikipedia article on the writer himself. I find reading about the auther often gives me more insight to their writing. ...Except for Hemingway. The more I read about how he treated other people in his life, the more disinterested I became in his writing. So, sometimes reading the biography backfires.