Since your close to Penn Station take the LIRR to Jamaica and transfer to Airtrain to the Delta terminal. Cost is about $13, trains to Jamaica are frequent and only takes 20 minutes, then 10-15 on the Airtrain. Taxi could take an hour and will cost $50+. Delta is Terminal 2 & 3 same Airtrain stop, I believe you'd depart from Terminal 3.
Since your close to Penn