First you don't need Syosset. You need the Oyster Bay branch of the Long Island Railroad. You will get off at Oyster Bay and it's a short drive to Laurel Hollow.
Now for the realities of life: According to a Newsday article published Dec.21, 2016 (local newspaper), there was a plan to charge residents $100,./month at 4 Long Island Railroad parking lots. The plan was scrapped due to strong commuter opposition. There was a Jan. 10, 2017 meeting by the Town Board but my advice is to Google this and follow up. Here is what I know as a life long NYC suburban resident (I live in Westchester County). Westchester County has permit parking at most MetroNorth train stations for weekday commuters. Commuters are charged monthly fees. Currently Oyster Bay and other Long Island Railroad stations do not charge commuters or require permits to park there. However, this is not guaranteed and it is possible at some point in the future, commuters will need to pay for parking at train stations. If MetroNorth does, then it is possible the Long Island Railroad parking lots will too.
As for the cost from Oyster Bay to Penn Station - $297./month; Time: 1 hour 20 min. If you don't commute to Manhattan daily, the fares are cheaper.
I know commuting is expensive but this is the "cost" factor of living in the NYC suburbs. The further out from NYC, housing gets a bit cheaper BUT commuting costs are more expensive. You can't win.