The cheapest way is a container that you load and unload yourself. We've done this multiple times. If you plan your load, your furniture will arrive in as perfect condition as it left the US.
You can arrange your own container or go through a shipping agent. Cost varies with origin/destination. If you are some distance from a container port, the road transport component will be greater that it would otherwise.
Beware the quotes for containers that are based on cubic feet and/or weight. A container is a container; it holds what it holds. A 20 foot container costs almost as much as a 40 foot to ship, as the road transport component doesn't vary and the sea transport is nearly the same.
