QCAD will start with its welcome screen where you can choose some default settings.

Per the installation instructions: QCAD will start with its welcome screen where you can choose some default settings. Once you confirm, the QCAD application window will be shown and you can start working with QCAD:

This happened when I downloaded the trial version but not when I downloaded the paid version. Is it something that needs to happen? QCAD seems to work fine. If it matters, I had uninstalled the trial version and deleted the download.

If you have already set up these things in the welcome screen of the trial version, you do not need to set them up again in the full version. You can change all these settings and more anytime in the application preferences (Edit > Application Preferences).