I’ve heard a few people on here are starting their own personal instances so they can federate independently with different instances without relying on a larger, third-party instance. If I wanted to do this, would I need to own an actual server, separate from my PC?
If you are going to be the only user, no you can put it on your PC. It become unresponsive when your PC sleeps. It will cache everything on the network you subscribe to (meaning that stuff takes up space on your hard drive), and if you create a community on it, the entire fediverse will depend on your PC being on and reachable, over whatever internet/WiFi you have at the time. Your need to buy a domain name and set up TLS certificates, and configure your router and firewall to safely allow incoming traffic.
There really is no upside to running and instance on a workstation PC other than development testing. You need a server, and they suck down electricity like you don’t even know (trust me, i have 3). Find a good and cheap VPS if you really want to get your feet wet with this. I vote for Hetzner but there are tons out there.
Or, check out the selfhosted community if you are interested in learning how to do your own servers. It’s a damn rabbit hole but can be very rewarding!