You might have difficulty shipping a standard 20 or 40' container by rail within the US unless it has a standard set of ownership markings on it.
(Not endorsing Fedex, just an example. Lots of other companies do this too.)
You could also consider hiring a moving company.
No, I've shipped pallets of freight before, using Fedex among others. The issue is that I've got one of these https://en.wikipedia.org/wiki/Twenty-foot_equivalent_unit, and I want to get it across the country full of stuff.
It's possible Fedex has provisions to do this if paid enough, but I think I'm looking for something more specialized. Like this, but I'm looking for more specific recommendations: http://rapidexpressfreight.com/freight-services/rapid-expres...
This is an important differentiator. Many other freight network startups have failed because they couldn't get the supply/demand flywheel turning fast enough. Integrating with existing carrier networks means you won't undercut them on price, but you can compete on convenience for shippers.