normally you'd rent out a server (vps) and run it on there but hosting from your house would also work. the whole idea about Lemmy is that each instance is ran on different servers by different people
I'd be hesitant to run it at your own house. While you can use a cloudflare tunnel, I'd never expose anything in my home network to the outside.
Digital ocean is cheap, there's another called hetzner which looks also pretty cheap. So you start will rent 1 core VPS for 5 bucks, it's enough to run your own instance but not really enough to host any communities.