The Train is OK if you're not moving anything that's time sensitive of perishable.
I formerly worked for a company that hauled RV's across the continent by Truck.
At one point RV's where moved by Train, but the RV season is only five months
long (for most people in most places in Canada), so the (I'm not kidding) sometimes
three month shipping time by train didn't work well.
If your budget allows, leaving your move up to the professionals at a moving
company is the way to go. You'll (I'd assume) have your hands full with your own
family, new job, getting the kids settled into new schools, etc....
If the budget doesn't allow, but time does....renting a Truck and humping your own
possessions is always an option. If you take the US route....the roads are better
and your trip's still about 2600 miles long, and you can have one Hell of an issue
with customs with a truck full of misc. un-itemized 'stuff' crossing the border twice.
I'd be shocked if you didn't have an issue.
The Canadian route is longer, with roads that can be much poorer in quality, but
it avoids the international border (twice) and the issues you'll almost certainly have.
This route is a bit shy of 2800 miles long, and that's a long time to be in a Truck by
yourself, but a longer time to be in the cab of a Truck with anyone else. Trapped in
a tiny space like that for several days with your wife (or wife & kids...) could be
enough to kill a relationship...as you can't avoid each other at the end of the trip.
If you can, hire movers....& either drive your own car or fly to your destination. Now
I'm watching for some helpful member who has just created an account today to
(by coincidence...;-)) start advertising their moving company (or hamming it up with
a fake testimonial about some specific moving company) on this SPAM free Forum.