Definitions:
LGA- La Guardia, closest to Manhattan, it is on the norther side of an outer borough of New York- Queens. LGA is dense, chaotic and very convenient geographically for Manhattan and points north.
JFK- Kennedy is the furthest of the three from Manhattan (but on the southern side of Queens), an international airport, and is sprawlingly large. It works best for the eastern suburbs of NYC.
EWK - Newark is in New Jersey, across the Hudson River from Manhattan. It is the newest of the three airports and it is the airport New Yorkers love to hate! But it the most orderly of the three.
Right now, in NYC, surface travel into and out of Manhattan is a real mess. Lots of problems due to the disaster area in lower Manhattan. My sons, who travel a lot, have taken to finding their way into and out of the airports by using trains. This is a more certain form of transportation but is A) incomplete and B) hard to explain on the Internet!!!
You can get to "rapid transit" trains from JFK and LGA, but to do so you must take a bus ride. Once on the train, NYC is an easy (and cheap) ride!
Without reference to public transportation, I would suggest looking for "Carey" private bus service. It is a major limo-type service that serves all the airports and has regularly scheduled buses, etc. to all areas. Also, you can share a cab from any airport to NYC. And there are detailed written instructions at each cab station at the airports.
I think the ground connection issue is, right now, of greater concern than which airport you use. AND in dealing with that, I would suggest trying to come into NYC other than in the early morning to mid afternoon time frame. If you can arrange to arrive in the evening, that will lessen your hassles a lot.
There are websites for all these options.
I hope this is helpful.