Researchers have built server prototypes that re-use old components

With these kind of servers you want to look at the idle draw. As a homeserver that is probably your 80-90% use case. Some of them draw a significant amount at idle as they are not configured to run that way. The next thing to look at is fans. They can be rather loud (but can sometimes be configured to run slower and less loud). Also many of them are rackmount items. So you will want to think about how to stack your machines. You can buy used racks or a halfrack or just dump them on a table somewhere. Also sometimes you have to worry about the power supply. Sometimes they use different power cables than what a normal house would use.

I personally moved about 10 years ago to a very simple setup using a intel nuc. The idle is in the 5-10w range and max 45-65. I was using something that was idle 100-200. It shaved off about 15-30 bucks off my power bill per month when I did it plus a couple of other items in the house that had very poor idle. I am planning to move back to something a bit more interesting. But the specs to keep an eye on is the idle and max draw. For me I want something modest. But if you go all out and drop a couple 4090s in there and a decent xeon or threadripper it can get up there. Also keep in mind some of them have extra interesting things like fiber channel cards or some sort of infrastructure fabric ports (or lots of sata). They are not 0 but do add into the cost. So you may want to look how to disable them if you are not using them.

So something that is ide 5w would be about 5 dollars per year idle and about 65 form my max load. My price per kwh is 11 cents. Pretty sure the formula is ((number of watts)/1000)24365*(price per kwh). That should get you the yearly cost. Just run the calc for max and min load.

So you may be better served buying something newer that uses less power in the long run. Short term though playing with old hardware can be cost effective and fun.