AFAIK Xen and KVM are free for personal use, and well supported in Linux and BSD.
Some distributions are using hardware hypervisors out of the box (though for other purposes). For example, Qubes OS
https://www.qubes-os.org/ is a Xen with a few isolated OSs on top (IIRC has both Fedora and Debian or so, for security and privacy reasons, and when you want to browse without traces it fires up a completely new OS install, with its own new browser, etc).
You'll probably need 2 displays/video cards/keyboards if you want to easily control a hardware hypervisor.
I've tried Xen and Proxmox some years ago, they all worked, but I couldn't pass the nVidia GPU to another machine, so that made the whole exercise futile, so I am still using virtual machines, but instead of VMware I am using VirtualBox (free to use for non-commercial). VirtualBox can open or import machines created with WMware, so you won't lose your old VM from VMware.
I'm using only virtual machines now, no hardware hypervisor, because I don't do gaming. The performance in VirtualBox is about the same as a bare metal install for my daily use of VM. Unless you are doing 3D video gaming from a VM, you won't notice any performance loss. I'm using mostly VMs isolated from the Internet and never updated, to preserve programming environments for devboards, compilers, etc.
Those VM can be preserved, and they will still work either with VMware or VirtualBox, either with Windows or Linux, nothing to install again or to reconfigure when you change computers/hardware, can be copied on a USB and run somewhere else, cloned, snapshoted, etc and all this from a nice GUI (some hardware Hypervisors only have a command line interface, or a spartan web interface at most).
If you combine VMs with a file system like ZFS (between other goodies, ZFS can do automated deduplication, so if you have 100 Ubuntu VMs 4GB each, with deduplication you'll need only a little more than 4GB instead of 400GB of disk).
No matter what method will work best for you, please come back and left your findings here, after a months or so of usage. I'm very curious if today, 3 years later, the hypervisor setup is easier than when I tried it.