virtualbox.org

When I run the VM, "No bootable medium found! System halted." What is the best source for a bootable DOS package, and how do I install it in the guest machine?

DOS in not supported in VirtualBox.
If you want to install it though you are going to need a copy of DOS. Search for freedos.

I've found and downloaded a copy of DOS 6.22. Question is, where do I put it so that VM will find it to boot from? Thanks!

Can't tell you that. If you just downloaded a copy of DOS 6.22 it is still licensed to Microsoft making it illegal to install.

Do I understand correctly, then that supported OS's are resident in VirtualBox? Can I install a licensed copy of DOS?

VirtualBox is only a program that allows you to install different operating systems. It does not come with these programs already installed as this would be against all licenses.
If you have a valid operating system that you own you can install it but DOS is not supported. See http://www.virtualbox.org/wiki/Guest_OSes for a list of supported guests. There are some here that have installed it and figured out how to make it work though but you really need to have extra files and know how to configure them to keep it from consuming all of the processor resources and causing heating problems.

For DOS better use DosBox. Its free and needs no Virtualiser.

There are How-To's for DOS under the Other Guests forum http://forums.virtualbox.org/viewforum.php?f=4