Lots of good discussions here about the future of containerization. One major point to keep in mind is that ocean-going containers are built differently than standard domestic containers. Ocean-going ones are much more sturdy since they stack higher and are exposed to corrosive sea water and much more harsher weather. Even with that requirement the cost of a steel open-sea rated container is relatively cheap - from around $3k for a 20' to around $4k (all in USD) for a 40' container. Costs, of course, rise and fall with market demand. This is the cost for one in a major port like Shanghai though, so building one elsewhere might incur a higher rate due to market, labor and other supply conditions.
Ocean-going containers are a major export to Asia from the US, though in many instances they go back empty. That rotation has varied depending on costs, and they have a finite-number of times to get used before they are scrapped or else sold off to become a storage box or whatever. I'd suspect you would be able to find empty containers at most any port that has an import/export market of any size.
I would assume most containers used for trade in Traveller would not be considered space-rated containers, so one would expect a Traveller-equivalent to be one that was built to the lowest possible TL standard in order for it to be built in as many locations as possible. Standardization is the byword of the Imperium and these would be no exception. Materials wise you'd expect them to be built of similar metal or even composites with enough structural integrity to transport their loads without issue. So they could easily be built at a TL-7 world or greater (TL-6 might be a bit too basic, though not impossible since we had similar ones in that timeframe in history). Being transported in holds means there is no need to build them to stand up to vacuum or exposure to radiation, which keeps their costs and TL down.
For container size I'd expect something similar to modern container standards - a half and a full-sized container (say 5dton and 10dton at 3m height). This simplifies all aspects of transport and handling. 3dton containers would also probably be around, if only for smaller ships and loads. While you may end up having smaller containers, I'd not consider them to be in the same class as the above ones.
Beyond that you'd probably see a mix of grav and wheeled vehicles for unloading. If you have access to grav tech (which any world would), one could attach lifters on top of either end or in the middle to maneuver the container in/out of a ship easily enough. Lifters of this type would be small enough to be carried onboad a ship for loading/unloading at lower-tech ports. Grav tech would free you up from having to restrict yourself to fixed-location container cranes or Mi-jack's on rails. You still may see such tech on lower tech worlds since it should be easily built and maintained locally and still works just fine for rail/trailer loads. For unloading larger ships you may see some form of internal grav-assisted loading mechanisms that would pick up and delivery containers to their storage locations. Even something as simpler as putting retractable wheels in deck plating (planes and air freight loading docks utilize something similar) gives you a large amount of flexibility with for a very low tech solution.
And, I'm sure, there will be new methods developed over the centuries with new forms of tech, just like it's been in our past.
