If its an ester based oil there is no reason to also call it synthetic- this would simply be redundant. If this oil is less than $10.00/qt there's probably very little ester in it, given the current cost of basestock.
Any shear stable, PAO/Ester based synthetic (Mobil1, Amsoil, Redline, etc), will be fine for this application. All things being equal the 10w-30 grades will tend to be more shear stable than their 5w-30.