If you want to go to the more relaxed, quiet, gay-oriented (although not all of it is) you_d want to take the ferry out of Sayville. It_s pretty much the same situation as with Bay Shore. Hop the LIRR to Sayville and take the ferry.
A day, starting very early in the morning is enough time to see your designated area... you_re not going to cover the whole island (you actually can_t, some spots you_d have to take a water taxi to get to)
http://www.fireislandcc.org/fitrans.html
You can take the LIRR (to exactly where I don_t know, i think it depends on what part of the island you are going to), but many people take a cab to the ferry, it_s not that expensive.
But, you say this is your first time to NY, so I say don_t bother. It_s far. It takes at least 2, maybe 3 hours to get there from the city. You will lose an entire day and you won_t see much there. If you don_t plan on spending at least a night there, you might as well just go to Long Beach. Fire Island doesn_t have many motels, it_s mostly timeshare homes.