The best way to play your iTunes music on an Echo is by connecting your device via Bluetooth. You can turn on your Bluetooth settings and ask Alexa to pair your device. You'll get standard playback controls through Alexa.
If you're more interested in a fully integrated Apple Music/iTunes experience, then I would consider taking a look at the Apple HomePod.
The device is very pricey ($349), but it's specifically geared toward iPhone and Apple users.