Multiple User Types - DB Design Advice
I would advice 1st one is better approach , which is 


Table: `users`; contains all similar fields as well as a `user_type_id` column (a foreign key on `id` in `user_types`
Table: `user_types`; contains an `id` and a `type` (Student, Instructor, etc.)
Table: `students`; contains fields only related to students as well as a `user_id` column (a foreign key of `id` on `users`)
Table: `instructors`; contains fields only related to instructors as well as a `user_id` column (a foreign key of `id` on `users`)
etc. for all `user_types`


Reason:-

User related data like columns in students, instructors etc tables may increase in future so it will be easy to manage with 1st approach. 

and choosing the other options to create a table with too many numbers of columns which would be not good in terms of future database management and with increasing number of columns in future it will more problematic.