Why does Paul emphasise that Jesus is the Son of David in 2 Timothy In 2 Timothy 2:8-9, Paul writes: 


  8 Remember Jesus Christ, raised from the dead, descended from David. This is my gospel, 9 for which I am suffering even to the point of being chained like a criminal (NIV, emphases mine)


From my reading of this, Paul's gospel is Jesus Christ, raised from the dead, descended from David. I understand why Jesus rising from the dead would be part of the Gospel, but why include descendant of David? Wouldn't something like Son of God be more important to have in your gospel?
Because Jesus descended from the family line of David.
As Isaiah says,


  Isaiah 11 English Standard Version (ESV) The Righteous Reign of the
  Branch
  
  11 There shall come forth a shoot from the stump of Jesse,
      and a branch from his roots shall bear fruit.


The Branch is Jesus. Jesse is the father of David. In fact many prophecies from Old Testament said the one to redeem Israel is from house of David. Often the Bible would refer Jesus as David.

Also remember the blind man that was calling out to Jesus, he referred to Jesus as "son of David".


  Matthew 9:27 [ Jesus Heals Two Blind Men ] And as Jesus passed on from
  there, two blind men followed him, crying aloud, “Have mercy on us,
  Son of David.”
  
  Psalm 132:11 The Lord swore to David a sure oath from which he will
  not turn back: “One of the sons of your body I will set on your
  throne.
  
  Matthew 1:1 [ The Genealogy of Jesus Christ ] The book of the
  genealogy of Jesus Christ, the son of David, the son of Abraham.