Running out of storage on my iphone6, what are my options?

Delete some stuff.

Store less stuff on your iPhone

Not sure what your question is then.

If you want to increase available space, then you would need to remove content.

What's the original storage capacity of your device? There may be a lesson there. Things you could try include storing photos in iPhoto and not on your phone, and the same for documents and movie clips in other repositories, such as iCloud or iTunes. There are other cloud based storage facilities as well, such as Dropbox. Something else to do is to sync less music - does anyone *really* need thousands of tracks on their phone, and delete very large apps that you seldom use, anything over 500Mb for example. You can always juggle things and re-download apps later.

If you go to Settings>General>Usage>Storage>Manage Storage, what is listed as taking up the most space?

Your iPad backup is not stored on your iPhone 6, it will be in your iCloud Storage. Make sure when you look at Manage Storage, you don't choose iCloud. Choose Manage Storage from the area titled Storage. That shows what's taking up room on your device.