How can I stop incoming e-mails interfering with music playback?
Because the iPod Touch doesn't have a Mute switch like the iPhone, you will have to disable all the alerts in Settings > Sound. This can be done by tapping "None" on each of the Sounds (i.e. New Mail, etc.)

If you have iOS 6, you can switch on Do Not Disturb. You can then customize the settings in Notifications > Do Not Disturb. You could allow all calls (Facetime for later gen iPods) by changing the "Allow Calls From" settings. However, there will not be any text notifications - or anything else for that matter.