Marvel Unlimited is a pretty fantastic value. But it doesn't have an parental controls and most of the stuff is geared towards young adults+. There a lot of a comics that are pretty violent on there. Don't think I've come across anything with sex/nudity.
The only other option is buying comics piecemeal from the Marvel or DC stores or Comixology. Comixology has both Marvel and DC comics and has the best app for reading comics so I'd recommend that. They also constantly have various series on sales there. I rarely see them put kids comics on sale but it happens every once in awhile. You can buy single issues, or in several cases bundles, and they just started subscriptions on some series. I don't see any parental controls but they wouldn't be able to purchase/download any comics you don't own without knowing your site or Apple password.
Here's a link to their kids comics - they have age ratings for each to them: https://www.comixology.com/Childrens/comics-genre/33