International moves are commonly charged on either weight or cubic foot basis. Packing services are usually charged separately, usually at a specific rate for providing each carton and providing the packing labor. There are many other services that could apply also for special services like hoisting, special handling of bulky items like cars or boats, servicing of special items like washing machines or grandfather clocks etc. I could go on and on. Payment to movers are usually done on delivery in cash or certified checks.
Some movers take credit cards.
None will take personal checks. If you feel your moving crew did a good job and want to tip them, by all means do so. It is customary to tip the driver and let him take care of his helpers. Usually, the helpers work for the driver. It is important to understand, tipping is not mandatory.