Taking public transportation, particularly at that hour, is totally fine - the buses and subways will be filled with people. NYC is America's safest large city by far - don't stress it.

I'd recommend taking the M60 to the subway - there's a Metrocard vending machine in the bowels of the main terminal, pretty close to the bus stop. It can be kind of a pain to find, though, so it may be easier to just pay the bus fare in coins ($2.50 now, I believe) and then get a Metrocard when you reach the subway.

Depending on where you're going, you can either get off the bus at the N station at Astoria Blvd (you can't miss it - it's a giant elevated train track looming above you) and take that downtown. Or you can continue on the M60 into Harlem. The bus will go down 125th St and give you transfer options to the 4/5/6, 2/3, A/C, etc.