Hey there,
it looks like you are running into a couple of pretty different problems.
First it looks like you are trying to use a couple of different providers. Vagrant won’t install a provider but once it is available and usable on the system they can be chosen explicitly using the --provider flag. eg. vagrant up --provider virtualbox.
The bit about libvirt:
libvirt: Error making a connection to libvirt URI qemu:///system?no_verify=1&keyfile=/home/stellaerrante/.ssh/id_rsa:
might be solved by restarting libvirt https://wiki.libvirt.org/page/The_daemon_cannot_be_started
The bit about virtualbox:
It looks like your virtualbox installation was not successful. Virtualbox has an installation guide (https://www.virtualbox.org/manual/ch02.html).