Good and valid question. So here is my take...
Using VEBF is a standalone solution that you will need to install in every VM. They are disconnected from each other and what you are actually doing is simulating a physical
Using Veeam Backup Free edition will give you the option to do true VM-level backups. No installation inside the VM, everything arranged from the host level. This is a completely different approach.
My advice here: take the time to browse to our resources on our site and get yourself familiar with the advantages, differences of backing up a VM on the host-level compared to doing it with VEBF and decide for yourself. Future wise, I would at least advise you to go this route. Use the correct tool for the job right
About the scheduling: Since update 2 (released a couple of weeks ago) there is PowerShell support with the free edition which makes scheduling perfectly possible