Hi saovry,

You can setting the quick registration by:
1. Click settings>general>login : https://www.screencast.com/t/MDZh3YwO2ThK

You can disable profile switching by:
1. Click profile types>select profile tye>disable profile switching : https://www.screencast.com/t/QwaytsY2T

Could you look at my attachment file.
Home is like that

Could I set the profile type to show up on the register page like that whenever admin choose quick or full register. The profile type show as drop down list so we can choose, we are student or teach...

Unfortunately that was not possible to populate choose profile type option in the mini registration form.

The current default behaviour is :

Full Registration form :
>> If you created more than one profile type , it will redirect to profile type selection page when you click on register link on the site.
>> screenshot : http://take.ms/on4pA

Mini Registration form :
>> For this mini registration form only available admin to set the profile type from backend setting, once you set this, when the user register from the mini registration form, this new user will directly registered in what you set the default profile type from the backend setting.
>> screenshot : https://www.screencast.com/t/DI7cMiEYb