What is the best sequence to apply for a Non-O Visa in Thailand: Should I rent a home, open a bank account, or apply for the visa first?

I'd say it doesn't matter except if you're using banked money here to meet the financial requirements and then you'd be needing a thai bank account when you apply.

I've had people get 90 day Non-O visas issued while staying in a hotel.

The big thing is you will need 15 days or more remaining on what every stamp you're here on to apply for a 90 day Non-O inside the country because it goes under consideration for 14 days before you go back to get the Non-O visa and the new 90 day admitted until stamp inked into your passport.

and you would be applying for a Non-O visa based on what?