As mentioned in the Insuring your international move section, if you choose to self-pack you'll be unable to claim for damages unless your shipment is a total loss. After all, from the point of view of an insurer, you don't have experience wrapping and packing and movers do it for a living.
Additionally, the more stuff you self-pack, the more likely it is that your goods will get held up in a customs inspection at your destination. Customs exams are usually not covered by the quote can add up to a big expense.
Make sure that the stuff you're shipping is clean, particularly if you're shipping garden tools, boots, sporting equipment, or items for a pet. Some countries will inspect your shipment for contaminants, and anything that can potentially bring in soil or bugs increases the likelihood that your shipment will be inspected.
If you plan on having the moving company pack your goods, make sure you check to see if packing materials are included when reviewing the quote. If not, you'll get charged separately and this can be a significant cost. When the movers arrive to your home to pack up your stuff, point out anything you want them to give extra attention to, like a glass vase or piece of art.
A good moving company will take inventory of everything they pack and make sure the number of boxes matches the number of things on this list. You'll need to review the list and sign it to indicate that it's correct; you should be provided with a carbon copy. It's a good idea to scan this (and any other important documents) and email them to yourself so you can access them in case they get lost.
Additionally, it's a good idea to document the condition of your stuff. The movers might write the condition down as they pack things up and provide a signed copy to you, but otherwise you should take photos or videos so you have proof in case anything shows up at your destination with damage.
Once your stuff has shipped, the international moving company will provide you with a document called the Bill of Lading. This will detail the vessel your shipment is on, the container number, and sailing details. This is the contract between you and the carrier, so make sure you keep a copy safe (see above: scan and email important documents).
The moving company will also provide you the name and contact details of a release agent. This is your contact at the destination and may be an office of the moving company you hired or a local moving company they partner with. (See How moving abroad works to understand why different companies may be involved). The release agent will contact you prior to the vessel's arrival at the destination port in order to arrange customs clearance and schedule pick-up or delivery services with you.
Every country has different requirements around customs clearance. In some the mover can clear customs for you and deliver your shipment straight to your new home. In others you're required to meet the movers at the nearest customs office to personally clear your shipment. Because of the differences, you'll need to ask your moving company what the rules are in your destination country.