Six year-old girl.
No time limit other than it needs to go away at bedtime.
She has her own kid's account on our streaming services on her tablet and some learning apps (ABCMouse, Khan Academy Kids, some Blockly-based beginner programming tools) and we gladly let her switch over to mom or dad's account if she's wanting to a kids' show that for whatever reason isn't on or got removed from the kids' side (e.g. Moana or Nat Geo's Weird But True). Our daughter is also welcome to watch recorded shows on the living room TV from our family's DVR.
She's also welcome to use phones and computers alongside mom or dad to call and video-chat with relatives or to look up information on the Internet.
We've taught our daughter that screens belong in the living room, to always ask permission if she wants to watch a "new-to-her" show on her device, which she's very good about doing. She also has our express permission to stop watching anything that she feels is too scary or otherwise makes her uncomfortable.
To combat the bad influences online, we have regular family discussions about the purpose of commercials and marketing, what's real and what's make-believe, that violence is rarely a good choice for any real-life situation despite TV, and that there are plenty of good people and content on the Internet but also some tricky ones that are out to hurt other people or steal their things: just like it is offline.
Having myself gotten onto the Internet in the early 1990s via "upcycled" computers and dial-up connections to local universities as a precocious tween with little parental help, I don't much faith in technological measures. As you might suspect, I was short on cash, rebellious, intelligent, and interested in all the wrong things online. Thankfully, those days were a lot more forgiving than our own time, and I ended up with a direct path to a career in software engineering rather untimely visits from law enforcement.
With that in mind, apples really don't fall far from trees. My daughter is already very interested in learning to type and wants to "write programs like dad," has her own ideas about how to efficiently guess mom and dad's passcodes, and is much more competent with social graces and persuasion that I ever was. I've no illusions about just how weak kids' accounts, Internet filters, passwords, or even netsec can be against a smart but bored kid with excess time on their hands.
For my wife and I, involved parenting, being truthful and upfront with our child, and modeling moral behavior has been our approach from day one. Besides, one day she'll leave home and will need to decide for herself.