Upgrading from PostgreSQL 9.3 to 11.6

I have a PostgreSQL 9.3 installation that I finally have time to migrate 
to a currently supported version. The server that the installation is 
installed on is also at its end of service.

Can anyone help me with completing this conversion as securely and 
efficiently as possible with the least amount of down time? Also, once 
it has been converted over, is there any best practice for ensuring that 
there has been no corruption?

The database is 600GB in size. We do not have any custom types being 
used.

Thanks for any direction.