I don't think it is a very good idea to straight run it to Secaucus, you would miss a lot of potential service areas.
I would imagine the line running like this:
An additional station in Chelsea or somewhere nearby
Tunnel to Hoboken Terminal with a station there
Some intermediate stops in Jersey City, preferably one near Newport and in Historic Downtown
Run through the Bergen arches, with a stop at Journal Square
Take the line to Secaucus, with a provision for an additional station at Harmon meadows and/or the Meadowlands (could be helpful once the mall opens)
(entering pipe dream territory) Or, why even stop at secaucus at all? If possible, end it at journal square and wait until an extension as far as Newark can be done. After all, Amtrak does not stop at Secaucus, and some NJ Transit express trains don't either. And the L train has a lot of possibilities regarding extension, it could run via Jersey City and Bayonne to Staten Island (although this probably is already being covered by the light rail proposal)
A train ride a day keeps the doctor away.