Unfortunately Proxmox doesn't use libvirtd, so Virt-Manager doesn't interact with it. It's designed entirely around using the web interface.
Your options here are to either stick with Proxmox without Virt-Manager, or use straight KVM. If you want a web interface for KVM, there's Cockpit, which is pretty decent for most basic tasks, but definitely a little lacking in advanced features, so you'll end up going to Virt-Manager for stuff like modifying virtual hardware. I think you can also use OpenStack as a web interface, but I've never played around with it myself.
Honestly, if you're a little newer to Linux I would probably stick with Proxmox, as it's a very well designed purpose built hypervisor.
For Docker, you'll want to deploy a VM and then setup Docker within the VM. Never run Docker from your hypervisor, it likes to fuck with IPtables in ways that break VM networking.