It may seem like stating the obvious, but it gets very hot in Spain and the mountains offer very little shade, so if you are fair skinned or someone who feels the heat, you need to take this into account. Light coloured clothes stay cooler than dark ones. Always wear long trousers or ones with detachable legs to cool off after a long walk. Lots of walks pass through scrubland that can be uncomfortable if the legs aren't covered.
Probably most important of all is a good pair of walking boots with ankle support and thick rubber soles. Many walks involve walking on scree and this can be very painful if one doesn't have proper soles.