Are you familiar with the Android Account Manager? [1] You can let users log in to your app with pretty much one click of an existing account. Since virtually every android user already have a google account signed in on their phones. It seems that using a google account would be the most obvious route for ideal user experience (no need to type in a new account you haven't before).
[1] http://developer.android.com/reference/android/accounts/Acco...