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My friend, Amtrak is mostly intercity and not many trains stop at Trenton. Your best bet will be taking NJ Transit's Northeast Corridor from Trenton to Penn Station New York. A one way ticket will cost you $20 ($40 round trip). There are even discount tickets available if you're going to be commuting every day.

Good luck

When I need to go to the city I just take the $1 bus so I wouldn't know about the amtrak. However, there is no point in you moving because your only traveling 3 time a week and transportation to NYC from Trenton should be easy.

New Jersey Transit (NJT) has rail service to NY Penn Station. The fare is $15.50, per trip to get to NYC ($31 round-trip), or $440 for a monthly pass that is also good on other NJT services (buses and the RiverLine).

The travel time to NY Penn Station is around 70 minutes on an express train or 90 minutes on a local train.

I hope this information was very helpful