Good morning dcuttler,
I understand you backed up your iPhone 4s uing iTunes and set up your iPhone 6 by restoring from that backup. If your music and ringtones did not transfer over, here are a few things you can try:
Manually sync with your iTunes Library
When you backed up your iPhone, did you transfer your iPhone purchases to your iTunes library? If so, all of your music (imported from CDs, downloaded from the iTunes Store) and playlists should still be in your iTunes library. You can choose which content you want to sync to your new device.
Manage content manually on your iPhone, iPad, and iPod - Apple Support
https://support.apple.com/en-is/HT201593
Download Past Purchases
You can choose to download any music that you have purchased from the iTunes Store to your new iPhone. Here's how:
Download past purchases - Apple Support
https://support.apple.com/en-is/HT201272
Ringtones
The article below will explain how to restore the ringtones you purchased:
Restore missing tones on your iPhone, iPad, or iPod touch running iOS 8.1.1 - Apple Support
https://support.apple.com/en-us/HT204076
I hope this information helps ....
- Judy