I take both the Amtrak and fly to Manhattan for work from the DC area, and I always try to figure out the fastest time from my house to my destination rather than trying for the cheapest flight or train. There are a few things that weren't mentioned yet that I personally think are important considerations. First of all, of the three airports, LGA is the closest to MVC by far in terms of time from the airport. As mentioned, JFK is a long and congested drive. Newark requires a trip through the Holland Tunnel and that means you have to go all the way across Manhattan from west to east. Also, Uber/Lyft are not right by the terminal at Newark or Laguardia meaning you have to walk a consideral distance to the pick up locations (I haven't been to JFK in a while so I can't comment on that). So for me it's Newark if I'm going to the west side (near the World Trade Center site) or LGA for anything east of Broadway. Newark to the Amtrak station is easy and inexpensive, but you would have to plan ahead to get the right train. If you've never been in the New York subway system, it's absolutely confusing and busy. I have co-workers who live in Manhattan and they have all of this transit stuff figured out, so it's second nature to them.
Thanks for your contribution to this thread, a thread that I've found to be far more interesting than I thought it would be. It's been a masterclass in good management technique as it's clearly proof that the best decisions are made after asking for everyone's input rather than one authoritarian boss making all his (or her) tunnelvision decisions.
Thanks for confirming above posts that LGA is "by far" the closest to Manhattan.
And that JFK "is a long and congested drive". Yet, it seems that the Airtrain link to the LIRR line (or the E train subway line if it gets you right to your destination) at Jamaica Station may make JFK a pretty good option. Assuming you're not buried in luggage and/or have six people in your party.
Taking a Newark cab may indeed necessitate a Holland Tunnel crossing. Or perhaps even a Lincoln Tunnel crossing which the GPS may "prefer" if its satellite indicates that the Holland is woefully congested and/or the Lincoln may provide an optimal route to one's midtown destination (like the Marriott Vacation Club). And the disadvantage of a Holland Tunnel crossing if you're going to Midtown is the distance south to north you have to travel, not necessarily west to east. You must be a Wall Street person.
Newark's own air train to the train that goes to Penn Station would likely work for the OP. The Marriott Vacation Club seems to be within walking distance, obviously depending on luggage and/or mobility capability.
If you happen to have a friend that can pick you up in Newark, I would recommend that you ask your friend to drive you to Boulevard East in Weehawken, Union City or West New York, New Jersey, just before you go through the Lincoln Tunnel. The view of Manhattan is world class.
But if you need to take a cab (in which case the cab driver may not allow any detours), you'll still see some nice "on the horizon" views of Manhattan.
But I did want to respond to your claim that the NYC subway system may be unfathomable to anyone that lives elsewhere. Not true. Just call the MTA and ask for a NYC city map to be mailed to you and you'll get the hang of it in no time.