The editions which provide a desktop without being a desktop is lxqt, lxde, openbox. They can fit inside an 8G VBox vm - maybe even less - I have not tried.
But a vm of 10G is the recommended as you usually has to account for some swap space too - but there is no restriction other than non-success.
I have made installs targeting a 8GB USB and it works.
You can try this one - probably easier than installing to USB by hand