One thing you dont want to do in New York regarding airport transportation is to take the offer of some guy who may solicit you for a ride from the airport. The cabs at all of the NYC airports are well regulated (usually its a flat rate to certain areas of town. Like midtown hotels, downtown hotels, etc) to not rip you off and I found the cost of a NYC cab to be similar to an Uber/Lyft.
You have 3 major airports in (or near) the city. Newark, which is technically in Jersey, but is really close to the city (IMO not the nicest airport... but it does have a nice convenient train station that you could take an Amtrak into the city for likely very little money) LaGuardia is located in Queens (which on its outskirts is very suburby despite being part of the city) and is a pretty nice airport. I like LaGuardia. Kennedy airport is also located in Queens and is the largest of the three I believe. And along with being the largest in terms of traffic, with a footprint that was built in the 50s, it suffers from some pretty severe congestion. Great airport. Crap design for modern airplanes with some pretty severe ground delays, especially if you're flying Delta. I have no clue why, but Delta and Kennedy do NOT seem to get along well on the ground. .
If I were giving advice on which airport to pick of these three it would be LaGuardia, Kennedy and then Newark. Just in terms of what airport is pleasant to fly in and out of.