Wake-on-LAN is probably what you want, if your specific hardware supports it which it probably does. This is a case of figuring out your exact hardware and a little RTFM-ing about how to enable and use WOL.

As for the drives it, in theory, would add more load/unload cycles to them and thus reduce their lifespan. But, in the real world, that almost certainly doesn’t matter, unless you’re turning the system on and off every 5 minutes: modern drives expect to go in and out of power saving modes and most controllers (especially usb enclosures!) do this pretty aggressively, so a couple more load cycles more-or-less are unlikely to actually cause your drive to fail any quicker than it would anyways.

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.