What are the oldest surviving manuscripts of the scriptures? Torah, Tanach, gospels, septuagint, dead sea scrolls, masoretic, whatever.

Which one is the oldest and how far?
the Ketef Hinnom is typically dated to 600BC - prior even to the fall of Jerusalem.  It only contains 3 verses, however.



In 1979, Gabriel Barkay (or more properly his 13 year old assistant), unearthed the Ketef Hinnom, a small silver scroll containing the blessing in Numbers 6: 24 - 26.  To wit, it is a traditional blessing still used today:


  “The Lord bless you and keep you;
   the Lord make his face shine on you
      and be gracious to you;
  the Lord turn his face toward you
      and give you peace.”’ 


It's text is essentially unchanged from what we have today, matching both the Masoretic Text and the Dead Sea Scrolls, which have been dated anywhere from 418 BC to 318 AD. (Personally, I favor the Qumran-as-an-Essene-community 200 BC interpretation.)

It looks like this.



In 2004, the scroll was unrolled and discovered to contain what is probably the oldest scripture we have - from 600 BC.  The primary significance of the fragment is to put a "latest date" of composition on the Torah.  JEPD traditionally held that the Scriptures were composed over various authors between 1000 BC and 600 BC.  This fragment shows this blessing, at very least, was in its current form, no later than 600 BC, although some scholars insist that generalizing the blessing to the entire book would be an over-interpretation.