For ultimate damage resistance, opt for tempered glass. Being considerably thicker than plastic (0.3-0.5mm compared to 0.1mm), it offers greater protection against cracks, scratches and bends. Plastic protectors, on the other hand, can provide adequate temporary protection on holiday, for example, or for your second or spare handset.
Finally, bear in mind that most screen protectors are designed to match specific devices. This includes cut-outs for components, such as headphone jacks, fingerprint readers, the screen etc. So be sure to check if the protector is compatible with your handset before buying.