Call the Public Works Dept for local wind loads - 90 mph min across US
Go to IBC/ASCE and find how to calc loads for signs. BTW - I would consider that a SOLID sign more than less.
Go back to IBC or other very good reference book and look up how to calc depth of post - BTW it is an iterative solution - so start at about 5' and go up or down.
That's what I would do - someone else may have a differrent idea(s)
ChipperB - I don't think you should ask for engineering design here. Ask for tips - direction - process. But asking for a direct design solution is not what this site is about.
San Antonio is actually right on the edge of a higher wind speed contour. If you are located in southeast part of San Antonio, you may be up in the 100 mph contour.