What should be my basis for selecting an airfoil?
For trainer aircraft, the major design driver in wing profile selection is stalling behaviour. Ample warning, docile &amp; progressive stall, no sudden surprises. Stall behaviour must be demonstrated during certification. From Torenbeek:


  The stall should preferably be characterized by a distinct and initially uncontrollable nose-down pitching motion, and during recovery to level flight it must be possible to prevent angles of roll and yaw of more than approximately 15 degrees (light aircraft)..


The NACA 4- and 5-series have been around for a while and there has been much experience with the application of them. Again from Torenbeek, fig 7-12:



Four-digit


  The NACA four-digit wing sections ... are by no means low-drag profiles, (but)
  the drag increase with lift is fairly gradual. The cambered sections have rel- atively high maximum lift and the stalling is fairly docile. 
  
  In view of the gradual changes in drag and pitching moment with 11ft, the 4-digit sections are frequently used for light trainers, which often fly in different conditions.


Five-digit


  The NACA 5-digit wing sections ... have the highest maximum lift of the standard NACA sections, but the stalling behavior is not particularly favorable and rather sensitive to scale effects.


This can be seen in the $C_l$-$\alpha$ curve B above, which drops off suddenly and dramatically after max $C_l$

NASA report CR-1646 has more information on the stalling behaviour of NACA profiles.