However, if your concern is primarily the historic influence of the English bible (not the influence of the bible in general on English literature), I would agree with the previous answer: the King James Version is without a doubt the most influential English bible. More: it is largely similar to earlier English bibles, and so for the influence of the English bible the KJV would seem to be best. The problem is that the KJV language is so archaic that it is difficult to understand – not on the order of Mallory, but on the order of 16th century English lit in general. The best King James Version in print at the time is the New Cambridge Paragraph Bible, also available in an inexpensive paperback
http://www.bibleselector.com/r_kjv_ncpb.html

IF you want the KJV but are looking for a modernized edition, there are some. The New King James Version is the most popular, but has some significant (to a Christian) differences from the original KJV (it is a new translation). Others that are much closer to the KJV (simply the KJV with modernized wording) are the "Easy Reading" version here
http://www.bibleselector.com/r_kjv_mc_es.html

the "with Word Changes"
http://www.bibleselector.com/r_kjv_ss.html

and the "Third Millennium" bible
http://www.bibleselector.com/r_kjv_apoc.html

The New Cambridge Paragraph Bible and the Third Millennium Bible both have the advantage of being "complete" KJV bibles. The New King James Version, the "Easy Reading" and the "with Word Changes" all abridge the entire Apocrypha.

Jim

P.S. Noticed faulty links. Repaired.
References :

Here is an online version of the King James version from the University of Virginia: http://etext.virginia.edu/kjv.browse.html
References :
Experience as a Christian