I agree to Mike,

In pattern like we fly today symetrical airfoils just don´t make the difference as long they are the same category, i.e. laminar or non-laminar.
The usually have similar delta alfa/cL and stalls and the same maximum cL. What makes them really differ is they behaviour in the near stalll. We do want a sharp stalling airfoil.
Also, we must be in mind that a the root and the tip airfoils are flying at dissimilar Reynolds number (i.e. the relative viscosity of the air) and the behaviour change as Reynolds number change.
More importantly is the wing platform and the correct positioning and dimensioning of the stab and rudder
One thing to experiment with is the use of symetrical reflex airfoils. By using them we could design very small stabs (10% of the wing area) and expect a very predictive airplane in the pitch axis (I think).
A great program to tinker with is the Profili 2. In it you can design, modify or just use the more than 1000 airfoils from the library. Also there is a implementation of the aerodynamic Eppler program that you could use if to visualize the polars and help you chose your airfoils

Dr. Wladimir