Check out JetKVM. The software and hardware is well thought out and works great. I use it for my homelab (mostly internally, so I can't say too much about external access).

https://jetkvm.com/

Here's a video comparison of 4 common options. He tests uploading an ISO, booting said ISO, looks at out of the box security and how the developers have handled issues.

Remote Access using IP KVMs! Full Comparison JetKVM vs NanoKVM vs Comet vs PiKVM

It might have intel amt or vpro already, which is out of band management.

Tailscale and ssh.

I use NanoKVM and I'm quite happy with that. Also connected to the internal header so it can power on/off and edit BIOS.

As for security, I don't allow its IP to open up any outgoing connections.

I use https://pikvm.org/

It’s a raspberry pi with a hat. Plugs into USB and HDMI to mimic a keyboard, mouse, and monitor, and you can wire it to the power button as well.

I keep mine behind a VPN for security but there are other options.

Responding as I also would be interested and don't want to lose this thread.

Though in my use case being able to power cycle is also important, although maybe could be done via controlling UPS

Mouse without borders? It’s Mickeysoft and somewhat flaky but it does the job. I use it for 2 local puters. Uses IP addresses. Maybe some swearing at your router to config it to work might do the job.

https://www.microsoft.com/en-ca/download/details.aspx?id=35460

So I've bought the nanokvm-usb. Why:

• I needed it quickly and was available
• the idea of going through another server for secutiry seemed better: I control the updates and security fixes
• well tested on the internet

the product itself costed around 50€ and I found a used mini pc with wireless connection for 25€

it was easy to install, works fine and is of good quality

You can use a smart plug to remotely control power to the Raspberry Pi.

If you enable Wake-on-LAN in the server BIOS, the Raspberry Pi can use Etherwake to power up the server when needed.

To connect to the Pi, I would suggest using a Pi4 or Pi5 and remote into it via Raspberry Pi Connect. That will give you secure remote access to the Pi.

ssh

though more seriously you haven't specified what platform the home server is. if you absolutely need a gui, probably VNC over ssh.