A different spin - for simplicity, with flight on time & no tarmac delays, etc. - best option would be, IMO, a car service (Dial7 or Carmel) booked on the spot with their free iOS/Android Apps as you plane is taxing to the gate @ LGA or while stepping off the jetbridge into the terminal - assumed you are traveling light on business with carry-on for this quick (client/account) meeting out in LI - the walk to the car service pickup / transportation area is about 5 minutes. Or, do Uber or Lyft - Carmel's fare quoted at $60 before online coupon discount of $3 or $4 plus tipping ... 20% usually for us.

It's a 22 miles trip & on Waze, showing travel time - door to door of about 35 minutes driving (or being driven by car service,) without dealing with MetroCard to get on the Q70 to LIRR (which at those PM hours, run about every 15 minutes for the connection to LIRR at Jamaica Station, and then connect to Garden City or Mineola with the final leg on a local taxi (or getting picked up at the station, etc.) - no stairs or escalators/elevators and long walks to/from the platforms. LIRR is quick & fast when it's running on schedule ... if & when it's not having signal or track problems, etc. etc.

Plane landed on time & parked at the gate by 2:15 PM, walk out to pre-arranged pickup for car service (drivers/dispatch often suggest to wait/meet on "arrival" level upstairs if at the "main" terminal) by 2:35 PM and underway on the parkway - could easily be at your Garden City location by 3:15 to 3:30 PM.

My preferred route as I do this on a somewhat regular basis since DW's HQ is out in Westbury & alternately, Hicksville - exit the airport, crossover on service road/ramp & head east on GCP (avoid the LIE or GCP) & head for the Whitestone Expwy - Cross Island Parkway to the Northern State Pkwy (avoiding buses & trucks on the LIE completely) toward Garden City - trip distance & time is almost the same as going on the LIE or Grand Central Parkway.

Afterward, head for the LIRR to Jamaica and then the AirTrain to JFK, exit for your terminal - go airside & relax, etc. Unless there are problems with trains, absolutely do not take car service - tons and tons reverse commuting, heading back out toward NYC ... (HOV lanes @ rush hours on LIE not of any help as it ends at city line !)