How do I choose the vertical tail's airfoil?
Normally, you would pick a symmetric airfoil. The thickness should be between 9% and 15% to find a good compromise between structural efficiency and maximum side force. Choose a thicker airfoil at the root, a thinner one at the tip and interpolate linearly between them.
Of course, for supersonic designs a thinner airfoil should be selected.
In some special cases a cambered vertical helped to improve flight characteristics, but this concerned mainly very powerful, single-engine propeller airplanes. I would expect your UAV is outside of this category.
Depending on the Reynolds number range of this vertical, a member of the Wortmann FX71-L series might be a good choice.