If you don't need a lot of resources, I would just get something very low power and an SSD big enough for your purposes, and leave it on all the time. Wake on LAN has never worked reliably for me (or at all, really).
Starting up is definitely where spinning drives experience the most failures. They'll run for tens of thousands of hours just fine, but one day if they stop, they might never spin back up.
You should also just measure your current power consumption for a baseline. You didn't say whether you have a 3050 tower, mini, or micro, but it's really the model of CPU that affects power the most.