My experience is a packing service is likely to not pack fragile items very well. If having to choose, a small indepentent (non-franchise) might be better. You should ask to see how they pack expensive delicate items and then deside. Once packed, the safest way to ship is USPS Registered Mail. It is virtually hand carried from point to point. UPS, FED-X, etc., you have to pack and allow for a long drop from a conveyor. That means, at the very least, that dropping the package from 6 foot, nothing gets damaged.
However, with Registered mail, it bypasses the regular system. It adds about $10 and the package must have all corners and seams taped with paper tape. Not every packer may be able to do this, but, it is safe, safe, safe, way to ship. My wife ships valuable, fragile, Reverse Glass Paintings this way. In addiction, sometimes I will build a plywood box lined with Styrofoam to protect the glass.
Another meathod would be to double box it so the inner box is protected with pellets or bubble wrap inside a larger box.
It all depends on what it is worth and how hard is it to replace. Insurance does not insure they will pay a claim. Many claims arise out of poor packaging.
Good Luck.