Technology is a necessary evil. While one could argue that it limits children, it also opens the world to them. Both children have iPods. They would love iPads, but it is too easy for them to access material I would prefer they not have access to until they are older. They are only allowed to use media in common rooms in our house. My husband and I check on them periodically and occasionally check the history on the computers. So far we have not had any issues. We do discuss internet safety regularly.
On dreary days, my son can play xbox online with his friends who are also confined to their home. At the same time, he can play in a room with people from different parts of our country and different parts of the world. Granted, they mostly talk about the game, but he also gets a chance to hear differing opinions from a variety of locations. When he was younger, the games were primarily educational and his time was very limited, not that it was necessary because he preferred to be on the go or playing with his building blocks and legos. Now that he is older, they are less educational and more fun/social. I'd prefer they all be in one room playing together, but that isn't always the case.
My daughter has a computer that she uses to compose and store the stories she writes. She does a great deal of research for both her story writing and school.
We don't watch much television and we don't have a DVR. If you don't want to make time to watch it the first time around, you don't need to record it for later.
As far as movies in the theater/cinema, that's something you may want to revisit later down the road. I know there have been times where there was absolutely nothing in the theater I thought my children should see. Conversely, there have been times where there were either a number of movies released that were worth seeing, or one movie they wanted to see more than once. Now that they are teens, this has happened more often. My 14 year old daughter saw Hunger Games three times in a week.
Technology is always changing, it's the nature of the beast. My junior year of school was the very first year that computer classes were offered, and the typing class used real typewriters and was not called "keyboarding." When our daughter was born, we didn't even have a cordless phone in the house, let alone a cell phone. Our internet was dial up and we'd only had that for a little over year. iPad? Heck no, it was a big, old bulky Walkman. By the time my children are ready to have children everything will have changed yet again. Enjoy your daughter and make your decisions as they come.