There are exactly two information we need for registration:
1.) E-Mail
2.) Password
If the user must write his email in an extra field (after login lol), you can also drop the twitter login button too as it is no simplification. Also there is no way to check against our database as the username (the email) is part of the password hash. No email, no password hash.
And as a third reason. Without the user email, user will not be able to reset the password if twitter is not available for any reasons or if the user has no access to his twitter account. So twitter button is out. We will stay with fb and g+.