What database use with my app

Edited: Updated - New Solution

I misunderstood your question earlier but the *note still stands – solution has been updated.
*Note; I am not familiar with postgresql
**Note: I did some research after the guilt of not understanding your question and answering what was not asked.

There is lot of reading that you will have to do.
Yes it’s possible to install it on the web server, follow link below on how to install, configure and connection string to us. Good luck.

1. Install PostgreSQL[^]
2. Configure PostgreSQL[^]
3. connectionstrings[^]