I would start with OpenDNS.
They allow family safe browsing. You can either change DNS at device level &/or router level. I recommend both on children's devices.
Otherwise a VPN may offer filtering of adult sites at a cost usually.
Then there's. Host file filtering, spybot, spyware blaster, ad blockers, and firewalls.
Many newer routers have family filters built into them.
You flcan also shop around for a different browser that has no incognito or allows it to be disabled.
Not any one on its own can protect 100% constantly. A layered approach of using a few of the above ways are recommended.
Also I do believe all images and flash, video can be denied but it makes a real ugly surfing experience.