I pretty much only use the mineral-based sunscreens (zinc oxide or titanium dioxide). The one I use the most is the Badger-brand, although it sometimes rubs off if I’m not careful. Doc’s is a bit more resistant to coming off, but it looks like they’ve unfortunately discontinued it. My SO really likes the Blue Lizard sunscreen, but most of theirs still has some other chemicals in there besides the minerals. Their baby version is purely mineral-based… I don’t know how it lasts though. I should get some and try it out. Their regular stuff definitely lasts, though.
Edited to add: I used Badger brand living in southern AZ, and now I live in the Bay Area of CA. I’m very fair-skinned and burn easily, so I am pretty paranoid about putting sunscreen on.