"Best" to me means fastest and safest. For all its faults, UPS seems to be the one I use more than any other.
Last year I shipped 4 balls in a 4 ball box to my hotel. I called the hotel first to make sure it was OK with them to send it there approximately 2 days ahead of time, in case of any problems with the weather or anything else.
I also brought my most valuable balls, one spare and one strike ball with me on the plane, along with my drilling specifications. Mentally and emotionally, you must be prepared for anything, like the box not arriving at all or being shipped to Sheboygan or Peoria by mistake. This is true for ANY and EVERY shipper.
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"None are so blind as those who will not see."