I do direct booking through the Houfy website, taking credit card payment by Square. 

Things like a website, an email at your domain and credible social accounts (even small things like a profile pic and bio) can show you are a legitimate business.

Columbus has an active following on this website so you are in the right place

With setting up LLCs would someone go to their Secretary of State website and do this?

Lancaster city limits short term rentals to only certain zones of the city so definitely look at the city website for that information.

If you can critically think, there's enough knowledge on this website to get you started for free.

Does anyone recommend knowledge sources on building a mobile home parks (websites, books, organizations, plans, etc..). 

She was very pleasant and explained that their website doesn’t work, which we thought was a bit unusual.

I was just on their website looking at the permit process:CityofSac-STR PermitLooks like 90 days max until you get a conditional use permit but still reading as it seems a little unclear:A short-term vacation rental may operate from a location that is not the operator's primary residence for a total of 90 days in a calendar year.

I wish there were more 'filters' / Criteria that you can filter by in real estate website to find what you're looking for.