If you don t want to buy ringtones or use the ones that came with your iphone you can create your own with itunes.
How to create your own ringtone on iphone.
Open itunes on the desktop to get started.
On your iphone open the settings menu.
This process changed a bit with itunes 12 7.
Choose the song you want to use to create a ringtone and click on it.
When the syncing completes your ringtone will be on your iphone.
Click apply then click sync in the bottom right corner of the window.
Go to the summary section.
Add the ringtone to your iphone.
Tap its name to set it as the default ringer.
Then select the iphone icon in the upper left corner.
To add the m4r ringtone file to your iphone connect your device to your computer using a lightning to usb cable.
Open the itunes app on your phone tap more bottom right corner and then tap tones.
Tap sounds then ringtone to see a list of all ringtones on your phone.