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Nanoparticles are a key ingredient found in most sunscreens (both titanium dioxide base and zinc oxide base). Within the broad family of nanoparticles made from these two minerals the effectiveness of sun protection and the potential for health concerns varies.
A 2016 report by the Therapeutic Goods Administration stated "neither titanium dioxide nor zinc oxide nanoparticles are likely to cause harm when used as ingredients in sunscreens". The report showed that nano particles in sunscreens were unlikely to penetrate the the skin.
Therapeutic Goods Administration
Avoid ingredients linked to skin damage - padimate O & avobenzone; and chemicals that can mess with hormones - benzophenone, oxybenzone, homosalate & octyl methoxycinnamate.