I don't want to use the QMainWaindow class, because I don't need DockWidgets or a menu bar. What would be the right class for an application main window instead?
You can use QWidget or QDialog. You will get most flexible solution with QWidget because it is base class for QDialog and for QMainWindow and many other widget classes.
BTW: you don't have to use dock widgets or menu, status, tool bars if you are using QMainWindow.