We present an investigation on ultrashort laser surface structuring with structured light fields generated by various q-plates. In particular, q-plates with topological charges q = 1, 3/2, 2, 5/2 are used to generate femtosecond (fs) vector vortex beams, and form complex periodic surface structures through multi-pulse ablation of a solid crystalline silicon target. We show how optical retardation tuning of the q-plate offers a feasible way to vary the fluence transverse distribution of the beam, thus allowing the production of structures with peculiar shapes, which depend on the value of q. The features of the generated surface structures are compared with the vector vortex beam characteristics at the focal plane, by rationalizing their relationship with the local state of the laser light. Our experimental findings demonstrate how irradiation with fs complex light beams can offer a valuable route to design unconventional surface structures.