First, before looking for a mover, confirm whether you need to ship everything: it might be cheaper to replace it at your destination than to pay for the cost of moving it. Additionally, many electronics will not work in foreign countries without power converters and plug adapters (and some television formats differ) so consider whether it's worthwhile to take these things with you. Think about how long will you be living in the destination country. Six months? Three years? Forever? If you're going somewhere for a short time, it may not make sense to take over all the comforts of home like artwork, books, etc.
Additionally, you should not ship the following:
Walk through your home with a notepad, selecting what you might want to move, sell, store, or give away. Knowing what needs to be moved will also be useful when you start talking to moving companies.