To tag onto this... for a low end VPS I love Hetzner. No, they aren't the cheapest, but the cheaper options are generally bottom-of-the-barrel unstable garbage or require promotions that expire. Hetzner is stable, professional, and cheap. Great choice for a simple personal VPS.
Super late reply here, but I was searching the Linux sub for vfio because I love this topic, lol. I'm happy to report that as others are saying, a vfio setup can be very performant! The GPU is near native, and with the proper CPU configuration, you won't be dealing with much overhead there either. The biggest factor is the overall load on your machine from running a host OS with the guest layered on top. I use my PC host OS primarily as a QEMU/KVM hypervisor, so when I need maximum gaming performance I simply turn off or suspend operation on all other VMs to free the resources for Windows. The only game I've had trouble with recently at 3440x1440 is Starfield, and unfortunately I think that is more a sign that an upgrade is finally due. I've used this setup for all kinds of games with no problem, including demanding virtual reality titles.
The biggest problem I've run into? Some anticheats truly despise any kind of virtualization. I've only run into issues with 2 games I like to play, but that is a real caveat. I consider it 100% an issue with the companies implementing these policies, who as I see it don't deserve my money in the first place. But other than the initial configuration headache and extra hardware required (if you don't have an iGPU anyway), this is the main drawback in my eyes.
The nice thing about an SSH tunnel is that it only exists when you create it, on the fly, per use, with your SSH credentials. And it is only accessible if you possess an authorized private key. An SSL connection through a browser doesn't fill the same role. SSL provides privacy and security in the communication between server and client. It doesnt have authentication built in. If you are accessing through a web browser you are probably talking to a web server, but SSH allows you to tunnel any protocol (web, rdp, whatever) forwarding traffic, encrypted, across a chosen port.
Edit to add a bit more: attack surface. SSH is a very robust and heavily used protocol with well tested implementations. Other solutions involving the web are probably involving software stacks with layers of configuration, more rapid iteration to add features and therefore a higher probability of vulnerabilities existing or being introduced in updates. Is this consideration relevant to your use? Probably not, =P but you asked about what might differentiate these two approaches from a security standpoint.
I have almost the same setup hardware wise. I got an RX550 GPU for the host, or sub in any cheap graphics card. If you have the spare slot and lanes its much nicer of an experience to have 2 GPUs. Plug a dummy plug into the guest GPU with looking glass set up and its great! :)
Just gonna add a bit here. I haven't used proxmox, but I do have a GPU I assign to QEMU/KVM virtual machines. The arch wiki has an article that helps a lot, for anyone who wishes to try this. I have also found that the virgl drivers allow for sufficient graphical performance for video decoding at high resolution, so that is another potential option to explore here that doesn't involve allocating the GPU to a VM.