Lifting a fully loaded container will be no problem, container sideloader trucks are not hard to find, maybe little more expensive than a ordinary truck to hire but not that much.
If the container will be moved at sea or port ares, it need to have a valid CSC plate and to be in a reasonable good condition. On a domestic road transport its only a "steel box" no CSC validity requirements there.
20 ft containers are typically structurally less prone for damages than 40 ft units, they also very often have a higher payload. For heavy "cargo " would go for a heavy payload 20ft unit, their often rated for up to 30MT.
If going to keep it as a storage, would specify the number of vents it has, some has only 2 whereas other might have 8. If you are going to purchase a used one, i would hand pick in the container depot(or at least request good photos) to avoid any surprises.