Surgient Success

The Surgient VQMS installer offers to install SQL Express as part of the setup. Do I have to install SQL Express to run the software, or can it use another database such as MySQL?

You don't have to install SQL Express to run VQMS.  While you cannot use MySQL, you can use any pre-existing MSFT SQL Server database server.  Supported versions are listed on page 8 of the install guide:

Microsoft SQL Server 2005 SP1
Microsoft SQL Server 2005 x64
Microsoft SQL Server Express
Microsoft SQL Server Express x64
Microsoft SQL Server 2000 SP4 (installed as
case-insensitive and using the 850 multi-lingual
code page)
NOTE:  Mixed Mode Authentication must be enabled, and remote connections using TCP/IP must be enabled

It is also recommended that during the install process you do not create an Database for the Surgient Product. The product will install the Database and User Accounts required.  It is also important to have a user account with both DB_Creator access as well as Security Administrator Privileges.