Flight
Newark is the United hub among the NYC airports. It's easier to get to Jersey City from here than the other airports, so it's a great place fly to/from if your hotel is there. However, if your hotel is in New York, be mindful that there's a charge for crossing the bridge, and there's generally tons of traffic when crossing between New York and New Jersey. Thus, if you need to cross, we highly recommend using the PATH trains first, and then taking taxis to / from the airport after crossing the river first.
Flight
Laguardia is generally the easiest for domestic flights, and it's the hub for for American and Delta air lines. It's in Queens, so it's generally easier to travel to / from if you're staying in the northern part of New York City. It's accessible via the 7/E/F/M/R lines to 74 St / Roosevelt Avenue stop followed by a transfer to the Q70 bus.
Flight
JFK airport is primarily for international flights and also serves as a hub for American, Delta, and JetBlue airlines. JFK is farther south than LaGuardia, so it's a bit better if you're staying in Brooklyn. Additionally, note that JFK has fixed fares to Manhattan for $52 for Yellow Cab (really around $70 after tax and tip), so if you're staying in Manhattan, it's also quite easy to travel to JFK. (Especially during congestion hours, cabs can be cheaper than Uber) Just beware of traffic.
Hotel
This is by far the most affordable accommodation in Manhattan. Located in the Chelsea area. Basic single-sex dorms sleep up to 4 people, and include linens, towels and shared bathrooms. Private rooms offer en suite bathrooms.