What is the best translation of the Mahabharata?

There is no single best translation, only the right one for what you want. Three kinds exist: complete scholarly translations, complete older translations, and abridgements.

Complete and modern: Bibek Debroy translated the critical edition in ten volumes for Penguin between 2010 and 2014. It is unabridged, readable, lightly annotated and the standard recommendation for someone who wants the whole thing in contemporary English. The University of Chicago Press edition begun by J. A. B. van Buitenen in 1973 is superb but incomplete; van Buitenen finished the first five books before his death, and later volumes by James Fitzgerald and others have continued the series slowly.

Complete and old: Kisari Mohan Ganguli translated the entire epic into English prose between 1883 and 1896. It is in the public domain, available free online, and still the version most often quoted, but the Victorian diction is heavy and it follows the vulgate text rather than the critical edition. The Manmatha Nath Dutt translation of the same era is similar in character.

Abridged: John D. Smith Penguin Classics abridgement is based on the critical edition and summarises the passages it does not translate, so the shape of the whole survives. C. Rajagopalachari retelling has introduced the epic to generations of Indian readers. R. K. Narayan version is shorter still and reads as a novel. These are retellings or condensations, not translations, and they smooth over the moral difficulty that makes the original interesting.

A practical route: begin with an abridgement to learn the names and the shape, then read Debroy or Ganguli for the books that interest you most, and read the Bhagavad Gita separately in a translation with commentary.