Which design to choose
I have read your question, but not your proposed solutions, so I can't be influeced.

So, my ideas is that you can do a table STUDENTS and another table, let's say STUDENT_TYPE.

In STUDENTS, you put a column, ID_STUDENT_TYPE. In this column, you can set, with the ID of STUDENT_TYPE, the type of the single student.

In this way, if you have to insert a new student type, you won't have any problems! ;)
It is an elastic solution!