Why Virtualize?

Before installing anything, it's worth being honest about whether you need this tier at all. Plenty of homelabs stay happy and functional running Docker on one box forever - that's not a failure to progress, it's Beginner working as intended.

What virtualization actually adds

A hypervisor like Proxmox VE lets one physical machine run multiple isolated operating systems - virtual machines and containers - each with its own allocated slice of CPU, RAM, and disk. Your Beginner-tier setup already has one form of isolation (Docker containers), so the real question isn't "isolation vs no isolation," it's what kind of isolation you need and whether managing more of it is worth the overhead.

Containers vs VMs vs both

Docker containers - share the host's kernel, start in seconds, use the least RAM/disk overhead. Great for the vast majority of self-hosted services (web apps, databases, media servers). This is what you've been using since Docker Essentials.
Virtual machines - a full guest OS with its own kernel, fully isolated from the host. Needed when you want a different OS entirely (Windows for a specific app, a BSD for ZFS reasons, a second Linux distro to test something risky), or when you want a workload to be unable to affect anything else on the box even if it's compromised or misbehaves badly.
LXC containers - Proxmox's own lightweight container type, OS-level virtualization like Docker but managed as a Proxmox guest with its own IP, its own boot process, and closer-to-VM management ergonomics. Covered in depth in Proxmox VMs and Containers.

"Both" is normal in practice: most Proxmox homelabs run one or two VMs (maybe a dedicated storage VM, maybe a Windows box) alongside several LXC containers, each running Docker internally for the services that don't need full isolation. You're not choosing one model - you're choosing which model fits which workload.

When Proxmox actually earns its keep

Reasons this tier is worth the added complexity, not just complexity for its own sake:

You want to isolate risk. A misbehaving or compromised service in its own VM/container can't touch anything else on the host the way a problem on a single shared Docker host theoretically could.
You want to separate concerns. Dedicated storage, a firewall/router VM, and application workloads each get their own boundary instead of all competing for the same OS's resources and attention.
You want snapshots and easy rollback at the OS level, not just at the container-data level - test a risky change, snapshot first, roll back in seconds if it goes wrong.
You're running out of one machine. If you've already got two or three physical boxes doing different jobs, Proxmox lets you manage them with one consistent tool instead of SSHing into each separately.

When it's not worth it (yet)

You're happy with one Docker host and it's not resource-constrained. More Docker Compose files on the same box is a completely legitimate way to keep growing - see Docker Compose Basics.
You don't have spare hardware. Running Proxmox well wants enough RAM to comfortably split between several guests plus the host itself - 16GB is a workable floor, 32GB+ is more comfortable if you're planning several VMs.
You want the absolute minimum to babysit. Proxmox is another system to patch, secure, and understand on top of everything running inside it. That's a real ongoing cost, not a one-time setup tax.

There's no penalty for staying on Beginner's single-box setup indefinitely. If you do want the separation, dedicated storage, and segmented networking this tier offers, the next step is installing Proxmox itself.

Next: Proxmox Installation.