Train travel is always a crap shoot. I have started out near Boston, got out to Worcester then gone west out of Worcester into Selkirk, then hopped east/southeast into NYC/NJ. Several trains, directions & hop outs. Alternatively I have also taken the chinatown bus many times to achieve the same trip for $15 in 5 hours from Boston. I guess it all depends on "if" I know "where" I am going or if I am just out wandering. For many the journey is in fact the destination but other times I know exactly where, when & why I am going somewhere specific.
I dunno about direct CSX to NJ. Even NS south towards Groton & the coast seems to terminate as much of the North/South coastal tracks are mostly commuter/amtrak.
If there is a southbound to NYC/NJ it may be on the PVD/WOR short line that could theoretically run south along the coast from WOR-PVD-CT & on into NYC. I heard there is such a weekly NYC run but unsure of anything beyond that. I cannot see such freight getting over to NJ.
I think it is all semantics anyway. Many of us who are bickering about specific trains & lines going here or there is just that. The reality is that there f there is a will, you will find a way. Often you will get lost & or find your way many hundreds of times before realizing that it is all just as productive. I second, third & or reaffirm that which has been said to the OP & all other greenhorns. Do your homework. Check the weather and plan to survive accordingly. The winter gear that is needed is expensive & heavy. Travel can be slow & miserable and not always the romantic version that we tell ourselves in our mind. I have long been a proponent of getting rideshares or taking busses to regions that are more conducive to winter traveling. I always advocate for common sense intermodal travel utilizing any & all available options where as some people will try to exclusively ride trains. We can wait days for our train or spend days riding trains in a roundabout way. The op is actually going to a predetermined place in Virginia where her uncle lives. I would suggest just taking multiple Chinatown busses. Bos-NYC, NYC-Norfolk, Richmond etc
It is all fine & dandy if you know how to not die and do not mind living on the edges of safety.