My 13-year-old child keeps asking me to buy him an iPhone. It is OK for me, but I don’t want him to access bad content or spending too much time with games on the phone. How can I do that?
You can go into the settings and turn on restrictions and then you won't have to worry. It will ask you for a passcode that your child cannot bypass. Also, if you want to block access on your home network, consider changing your DNS servers in your router to OpenDNS. Then, you can block all kinds of content at the router using their web interface. OpenDNS is easy and free, plus it can protect your whole network from phishing, malware and other malicious sites.
Use this your all problems will be solved.
All your concerns have been addressed by Apple. Kindly check out Apple solution for your concern at http://support.apple.com/kb/ht4213
Also you can install 3rd. party parental control software from iTune store, lot of them are available. For example, Kaspersky Parental Control (SafeBrowser) at https://itunes.apple.com/en/app/kaspersky-parental-control/id505542689?mt=8
The Safari Web browser on your iPhone keeps a log of Web pages that you have visited in the past.
SmyleSafe: Web Filtering Software