I would say with UPS - don't ship anything fragile. If you can't live with it breaking - don't ship it. Your mom's China - take with you (and for that matter don't put under the plane either). Don't ship anything that if they lost it (fragile or not) you'd be heartbroken. Make sure you insure everything with UPS - if you ship your cd player, put the insurance on it in case it breaks. I used to work for UPS and would still use them for most of my shipping. With the amount of boxes that came through, I was always surprised at how little broke. Of course, some of the stuff that broke was really important to people (mom's china), but to a certain extent, if it is that priceless, I don't think it should have been shipped. You know in advance that things can be broken. If you can't be the one that something breaks, then don't ship.
Make sure you keep your reciepts for insurance/shipping/etc. If something does happen to your boxes, you need the reciepts just in case UPS/FEDEX/whoever you go through needs to "prove" you had insurance.