How to configure MS SQL log on so that it can be used by another program?
Those options equal to:


windows authentication -> use a Windows (or domain) user account to connect to the database. Here you need to ensure that the user that runs the application (or the user that is configured to start the service) has access to the SQL Server (if you installed SQL Server and you're also installing the application, than most likely you already have access);
sql authentication -> create a SQL user that has access to the SQL Server and use it inside the application's connection strings. It is not dependent on the Windows/domain users, it's local only to that SQL installation.


If you're installing a new application that you're not familiar with, and it requests SQL Server access, then I suppose you should use Windows Authentication and check that the SQL Server service is started and accepts connections from that user. In SQL Server Configuration Manager you should check that the main SQL service is started and that it has enabled the main client protocols (TCP-IP and shared memory).