There are many fine translations of War and Peace available in English, and my recommendation is that you choose the one that you think you’ll enjoy the most and that will make you want to read the novel from beginning to end. And you needn’t fret too much about your choice: Tolstoy is one of those writers who loses surprisingly little in translation. His lucid prose, utterly recognizable characters, and universal truths seem to speak for themselves in any language, and through any translator.
Nevertheless, my personal favorite translation of War and Peace is the one by Richard Pevear and Larissa Volokhonsky, published by Alfred A. Knopf. It is scrupulously accurate, it beautifully captures the stylistic subtleties of the original novel, and it is wonderfully readable. That’s the translation I recommend to my students, and the one I suggest you try first. In this book all the citations from War and Peace are from the Pevear and Volokhonsky translation.