How are empennage airfoils chosen?
Selection of the profile is only a small portion of the design procedure of the empennage:


Aerodynamic centre of the aircraft minus tail is determined first.
Aft Centre of Gravity is determined.
Static longitudinal stability criteria determine the area of the empennage - upon a disturbance in Angle of Attack, the total aircraft must generate a moment that counteracts the disturbance. Usually, wings and fuselage contribute negative stability, and the tailplane must be sized such that the stabilising moment compensates for this in all circumstances.
Once the area is determined, the aspect ratio, taper ratio, sweep angle and profile thickness are chosen considering a host of factors, including the lift-curve slope, stall behaviour, out-of-trim conditions, structural weight, design diving Mach number.
And then the airfoil shape is chosen. From Torenbeek section 5.5.1.d:


  The basic requirements are that the airfoil section should have a high $C_{L_\alpha}$ and a large range of usable angles of attack. Frequent use is made of approximately symmetrical airfoils with a thickness ratio of 9 to 12 percent and a large nose radius, e.g. NACA 0012. Tailplane stalling - at
  the lower surface - can be postponed by adopting negative camber (e.g. NACA 23012 upside down), upward nose droop, an increase in the nose radius or by means of a fixed slot.



Table 9-2 from the same book contains (dated) horizontal tailplane design data and lists some profiles used:


Cessna 177: NACA 0012/009
Fokker F27: NACA 63A-014 mod.
Lockheed C-130B: NACA 23012 inv.
Cessna Citation 500: NACA 0010/0008
B737/100: 12%/9%
Boeing 707/320: BAC-317