It all depends on how much money you want to spend. If you want the fastest and the easiest way, take an Uber/Taxi/Lyft to and from the airport - it should cost somewhere in the $35-$45 range (depending on traffic and tip) to get from LGA -> Times Square, and then $60 to get from Times Square to JFK.
For something slightly less expensive, I would recommend
https://www.nycairporter.com/ourserv...-to-manhattan/ - it's not the Ritz, but it will work.
If you want to go the scenic route, I would still recommend taking a taxi/shuttle from LGA, transit options suck. Otherwise, just land in LGA and plug in your origin and destination on Google Maps. Their public transit directions will take into account closures (especially on Sunday, where things can get weird), and will be fairly accurate.
To JFK, you're either looking at taking a Taxi ($60), or a train (Subway: 1/2/3 or another, use Google Maps) down to Penn Station, and then the LIRR over to Jamaica, where you'll catch the Air Train. This is a pretty civilized ride, but isn't significantly cheaper with two people.
Hope that's helpful, happy to answer any Qs.