I have an ipod touch and I use the extended password option. My wife has half the password and I have the other half. Under the restrictions option you can turnoff wifi. You can also block turn off you tube and the internet browser app called safari. You can download the free k9 filtered browser from the app store. You can also set restrictions on apps, tv shows and movies, or turn them off totally.
All of these protections are the minimum for a frum person. That being said why should a teenager have their own device, it is such an incredible time waster.
On the other hand it can be a very useful and powerful tool when used properly. For the music and shiurim, you can get many other mp3 players. Even if all of the internet issues were taken care of, I think the temptation to waste too much time is too great.