If it's this cheap to run you don't need analytics because you don't need to monetize it, and if it's this simple you don't need logs because it'll all work correctly the first time!
"You don't need to monetize it" who's going to fund your Twitter-as-a-charity? What happens when the free money goes away? Businesses have to pay the bills eventually one way or another, you need to plan for that in advance
