Which is the best way to go from La Guardia to Manhattan

Karlson's answer certainly wins out in terms of money...

but for comfort and speed, with four people, each carrying luggage, I'd say a Taxi will probably win out handily for comfort and speed. Going from LGA to Midtown Manhattan should cost about 30-40 bucks (total), including tip, depending on traffic, and the trip should take about 45 minutes. Arriving at 9AM, by the time you get your luggage curbside, you should miss the worst of rush-hour, hitting whichever bridge you take at 10 or so.

When you exit baggage claim at LGA, there should be a prominent taxi stand where you can simply hop in line, and will be paired off with a cab - there are minivan taxis in circulation that you should be able to request if the extra cargo capacity for your luggage is an issue - no price difference, but you might have to wait an extra few minutes.

(If you do need that larger taxi, going back to LGA might be a bit more difficult - getting a minivan cab from a street hail can be hit or miss. If your hotel has a porter at the door, they can easily hail one for you while you wait inside without issue though. If that's not an option, Uber/Lyft/Livery Services will all offer you a larger vehicle at a comparable price without much issue.)