We quickly discover that her daughter went to school with my wife, and then she proceeds to tell me how the basement had been some sort of sex trade / flop house.

I don't want felons, drug dealers or sex offenders in my rental even if they pay the money!

Since I also live here, it is my understanding that I can select a same-sexed tenant as well as not have kids/other sexed overnight guests.

Sex and the City culture has been replaced by app culture where youngsters don't need to be right next to each other to meet like minded people.

However, this is still very new and being discussed as excluding violent criminals and sex offenders. 

Former "Sex and the City" actress, Cynthia Nixon is running for Governor of New York.One of the planks in her platform is UNIVERSAL RENT CONTROL - the implications of which are obvious - a stranglehold on rental property pricing in exchange for gaining tenant votes.https://cynthiafornewyork.com/issue/rent-justice-f...

In addition to that, we like to check with the police, fire, insurance, sex offender status, and anything that might affect the operations of the park.

I would go with cheap Male/Female or any sex large rooms, with a joint bathroom and kitchen area. 

Another tenant did this and the couple were "sex workers" where she was the main one working and he was her security. 

My roommate agreement specified things like: furnished or unfurnished, maximum occupancy- limiting number of overnight guests as it's bills paid roommate living, if it's co-ed or single sex, no smoking vaping e-cigs or substances on the property, cleaning chores/expectations, no underage drinking, pet rules, what utilities are included up to what limits and what utilities aren't included, etc.Require a security deposit from each roommate, even if small.Get a locking thermostat cover; set utility allowances so people won't take advantage of "all bills paid" rooms and have the daughter/master tenant or whoever is paying the utility bills be the person who sets the utilities.