I just bought a decommissioned computer from a public institution for 40€ (they are usually relatively cheap and still top modern, since companies replace their computers after 2 to 4 years, for tax reasons).
For this I just bought 2 HDD hard drives (I can only put 2 in; they are relatively cheap in comparison for a lot of storage space) and a nvme2 ssd was already included, there is the OS on it.
To make the server publicly accessible with a private internet connection (not a business connection), I bought a domain (I bought it at namecheap) and then I set up DynDNS at my domain provider and my router. This was relatively easy (with namecheap and a FritzBox).
I added a DNS entry that forward all subdomains to my DynDNS. The software, I want to have installed, I then simply install in a docke/ podman container and make a reverse proxy to the docker container via Nginx. This allows me to let multiple applications use the http(s) port from the outside via subdomains, so the URL doesn't need a port.
I can post the specs later, with an edit.
Edit: I don't know how much the electricity costs, because I currently don't pay for the electricity. But I have a 200W Power Supply and the machine is idling around a lot, as the service just not often used, but sporadic.
I am running Ubuntu server and I am... satisfied with it. It does what it should, no problems, nothing to worry about, stable AF (as any mature distro?). But lately I am thinking about switching to fedora server (I need to reset my system one way or another, because my space on the hard drive for the system ran out of space (it was a small drive)). I am using fedora on my work machine and I really like it, so I thought I could give fedora on my server a try.