I was originally going to host my instance on my own hardware but decided to use a $6/mo droplet on DigitalOcean. Seems to work well enough for me and my LCS bot. Picked up a domain off Google Domains for $20/year or so. It’s been a fun project and I’ve learned a lot along the way.
If it’s cable internet and not fiber/DSL, I’d look at connecting the ISP’s coax to the house’s coax. Provided all of the house’s coax ports are connected to a splitter, you could feed the ISP coax into the nearest port and plug the cable modem into the office port.