Hi, wondering I can get some advice on transportation for 1 person from JFK to Times Square. Coming in to JFK late so will be staying at a JFK airport hotel. Not real versed on taking subways...would it be safe to take Airtrain or should I rely on airport bus transport...

Can you advise on the following on who to take, where to pickup and what time should leave to meet, and cost, etc.:

1) Best transport from JFK to Times Square (on Sat. morning into the City).
2) Best transport from Times Square to JFK (Flight is 9:15am on Sunday)

Can you advise where closest station to pickup (Grand Central, Port Authority, etc). Would I be better to take the airport bus? If so, how early would I have to leave to catch a 9am flight out of JFK on a Sunday?

Thanks in advance for your help!