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.
Listen to this guy. Most LED tape is 12V or 24V. A 5V 20A power supply may meet your wattage requirement, but the LED tape will need it at 12V to function properly.
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.
If you have a local audio/video company, give them a call. Most of the big brands have a whole product line geared towards hospitality use that gives much greater control over "smart" features. They're usually not available to the general public, but an A/V dealer should be able to hook you up