The issues we face around devices in the modern home are a frequent source of family discord. It is so well documented that temper tantrums thrown around devices are called "iPaddies".
You have some distinct choices to make in this.
These choices have both positives and negatives. I suggest that you take option two. The reasoning behind this is simple: you cannot always be there to control a child. We want our children to make good choices when we are not there to guide (or force) them. It is far better to enter an open discourse cocncerning the risks and benefits of internet/gaming/device use.
I am afraid that this model is no longer good enough for our modern world. I am not sure it ever was.
But I am aware that trying to deal with these issues takes a lot of parents out of their comfort zones, but that is something you will just have to deal with.