What’s the oldest complete extant manuscript of these books? The Greek or the Hebrew?
Seeing as the earliest writings were done on animal skins, which deteriorated over time, we don't have the "original" autographs. What we do have are copies, sometimes copies of copies. What has survived today is:
2. The Samaritan Pentateuch: Written in paleo-Hebrew, this work only involves the first five books (Torah), the version could be dated to the 3rd to 2nd century B.C. The oldest existing manuscript is dated to the 13th century.
3. The Qumran Manuscripts (Dead Sea Scrolls): Manuscripts found at the Dead Sea, dating between 250 B.C. to A.D. 50. A portion of every book of the Bible except Esther has been found at this site.
4. Ancient Hebrew Manuscripts: Other ancient Hebrew manuscripts have been discovered, in addition to the Dead Sea Scrolls. These include the Nash Papyrus, Masada, Murabbarat and the Cairo Genizah).
5. The Septuagint: (250-100 B.C.), the Greek translation of the Old Testament.
6. OT Greek Manuscripts: Aquila, Symmachus and Theodotion.
7. Syriac Peshitta: Dated to the 1st century A.D.
8. Jewish Targums: Aramaic paraphrase translations of the Old Testament 3rd and 4th centuries A.D., These translations have a much older tradition dating back to the time of Ezra possibly.
9. Latin Vulgate: A.D. 390-405, Latin Translation by Jerome. (from http://www.truthnet.org/Bible-Origins/10_Old-Testament-Tanakh-Manuscripts/index.htm) This site also lists the history of the parts of the ancient manuscripts including what they contain.