I'm designing a fixed wing UAV and I'm having some doubts about how to determinate the vertical tail airfoil. It's important to say that we've already sized this surface. And till this moment we're using the software XFLR5 for the analysis.
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.