Containers are the cheapest option, and it is door-to-door. BUT - you pack, load and unload. We've done that multiple times, and as long as the load is planned well, it's not that difficult. You have a a specific amount of time to load/unload; time over incurs extra charge, but it's not onerous. A 40' container will typically handle all the 'stuff' in a 3BR house, including personal effects.
The easiest way is to find a shipping agent who will arrange the container. If you are some distance from a container port, the road transport cost can be hefty, but I've seen recent quotes on another site for a near-port location running under $3K. The Fx rate does affect the cost.
You need to pack well, number your boxes, and have a pretty detailed list of what's in each box. Doesn't have to be "12 plates, 4 cups, 3 saucers, 22 forks" detailed, just "assorted dishes and cutlery"; "assorted clothing" - that kind of thing. You need that list for the C-3 custom forms. Time varies with port and container line, but think in the region of 4 to 6 weeks.