. $160k in FL, you will have to leverage and furnish.

Would a setup where a historic building with 7 rooms, 2 bathrooms and a kitchen is rented out by the room exclusively to air force personnel, potentially furnished? 

You might want to start with just one unit, since you'll have to lay out more cash to furnish it, etc.

The thought process is to buy a new condo or a town home, furnish with a high-end package, go with an established marketing / booking agency - and command higher rents.

Airbnb is more management and you would need to furnish, but rental furniture is a possibility.

Getting the property furnished, stocked, rented out and serviced between occupancies is the hard part.

What's the going rate for a bedroom, with furnished living room?

Resident shall be responsible to furnish light bulbs for fixtures.

I'm a little leary to think that 6 nights (3 weeks * 2 nights) is going to be enough to cover mortgage, insurance, property tax, maintenance, cleaning, furnishing, 100% of utilities, cable, internet, etc. but maybe I'm all wrong. 

That, in a nutshell, is what you are allowing someone to do.You could let them do it for 12 months, learn from them, then convert your other properties into STRs.  6 years ago I got lucky and was able to charge $840/week for a furnished 2 bedroom house that normally brought in $350/month as a LTR.