Something like an old laptop will make a power-saving homeserver. But that won't work if you want to attach lots of storage.
I don't think an Optiplex is the most energy-efficient choice. They seem somewhat okay, but you'd need to put some effort in and read some tests and reviews to find a really efficient mainboard and PSU. That's not easy
You can spin down your harddisks. I have some udev rule that executes hdparm -S60 /dev/sdb after boot. That'll spin down the hdd after 5 minutes of inactivity. It's alright for low usage scenarios. And it doesn't spin up that often because the hdd contains my photos, backups and a few movies. And my operating system and files that are accessed often, are on a SSD. Starting and stopping disks like once a day should work for many years. But don't cycle it every few minutes.
And obviously, you can also shut off your server over night or just wake it on demand, if that fits your use-case.