Hello, I've lived in New York for 6 months in Upper West Side Manhattan. I traveled back and forth 3 times since I've lived here and I can tell you... anytime is rush hour unless it's in the wee hours of the morning and you don't want to travel during those times anyway (a little scary and intimidating to newcomers). If you want to avoid some of the hassle of the train system.. although it is quite good.. but a bit confusing if you do not know your exact route, I'd suggest the SuperShuttle.. they have a website, just google it. It's about $23.00, tip included and they'll take you from the airport to your door. I've done this twice. Coming back from the airport on the shuttle usually means it will take a bit longer since they'll most likely pickup a few passengers (up to 11) but it's efficient and cheaper than a taxi (around $40).
Quick note: the train can take you up to an hour and a half, where as the shuttle usually gets you home in under an hour.
I didn't have a chance to read all of the replies so if this is repeated information, please forgive me.