I’d argue that beyond the distribution itself it’s a lot more about what you install that will make the difference. If you can basically stick to the console and connect via ssh you’ll have a lot more resources available, both bandwidth (assuming you were planning to see a remote desktop) needed but also disk, CPU and RAM. There are lightweight WM e.g ratpoison but IMHO a server should be headless.
So… yes Debian but IMHO Debian without any desktop, just boot with sshd running, Ethernet cable plugged in and connect remotely.
PS: I’d also check if a RPi could be sufficient. I’m running few RPi4s and RPi Zero with 100Go+ microSDs and that’s very small, silent and doesn’t consume much energy. I understand it’s appealing to upcycle old hardware but in the long run, e.g 1 year running 24/7 might not be worth it.