The correct answer would really depend upon the application and size of the database.
The “BEST” DBMS might be a bit expensive if you have 3 users and only a small number of files with only thousands of records.
What are the experience levels of the staff?
Will you be hiring a new employee to be the DB Admin?
Are you writing a new application yourself or buying something off the shelf?
Please give us more information and you will get a more specific answer.