I liked Belinda's response re: "Media Time". We have the same, we call it "Screen Time". This covers movies, TV, computer time, and video games including those played on a TV or handheld.
Our kids (ALL ages: 14, 12, 6, 4, and 2) get 1 hour a weekday. They have to set a timer on the oven in order to use it. The older ones used to use old Chuck-E-Cheese tokens to buy 1/2 hour per token. They are not allowed screen time unless chores and homework are done.
On weekends we will often watch a movie which obviously takes more than 1 hour. But we limit it to that.
The reason is that the olders (my stepkids) go back and forth between homes. They do not have restriction on screen time at mom's house, yet they both have struggled severely in school. We believe it is directly related. (Homework is not turned in, yet they can always tell you what happened on their favorite show the night before!)
I also read an article about the way shows are filmed nowadays, there is constant motion. There are multiple TV cameras and they jump from one angle to the next. In the past, this was not so. If you want to see what I mean, compare a typical kids' show today (or any TV show) with Mr. Rogers Neighborhood. His show is very, very slow in comparison. There is no jumping between cameras. There is one camera which follows the entire show, for the most part. I can't remmber their technical name for this particular effect, it was like the flash effect or something. What it does is train kids' eyes and brains to want constant motion, very active, etc. This supposedly contributes to ADD and ADHD. I can't say what the scientific research is to back this up, but it seemed to make perfect sense to me once I compared the TV shows.
To report in on how well it has worked with the stepkids, they do not question our screen time policy at all. They stick to it, and no questions asked. My kids try to push the package a little more, but we try to stay consistent.
Honestly, I would like to use the TV as a babysitter more, but I try not to.
Best of luck to you as you decide how to proceed!