What trend does the first ionization energy follow, going down the periodic table?
Ionization energies decrease DOWN a Group of the Periodic Table.
Across the Period (from left to right when FACING the Table) ionization energies increase due to increased nuclear charge. A FULL valence shell of electrons shields nuclear charge effectively (which is not the case for an incomplete shell ACROSS a Period), and thus down the Group, it becomes easier to remove the valence electron.
Very simple notions of electrostatics would support this principle.
As chemists, as physical scientists, we should look at the data: this site describes the trend well.