You might want to define "long term" for parking. Overnight is OK.......30 nights in a row may have your car towed. If you are going to reside in the Rumson area, I would recommend using a taxi to and from the train or ferry dock when you planned to be away for any time. I live in Rumson and have taken a taxi to both the Red Bank train station and Highlands/Conners ferry. Both run about $12.
If you get to the Red Bank Train station very early (usually by 6:30am) you can Purchase parking for the day. Or you can sign up for a parking permit. The waiting list is about 3 - 4 years long, the cost is over $300 for the year. I hope this helps.
Parking at New Jersey Transit stations varies... your best bet is to check out their website (http://www.njtransit.com/rg/rg_servlet.srv?hdnPageAction=Tra ) for specific information including rates for the stations that are of interest to you.
Hope that helps!
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