I love ups but there are some problems with sending eggs. Ups is a bit unclear on whether eggs are even allowed to be shipped. Under live animals all birds are prohibited but it says nothing about eggs. Someone else said ups does not accept hatching eggs. You could just not mark they were eggs but the 2nd possible problem is that all ups 2day or less shipping options are by air. The eggs would be going on a plane with pressure changes. Some people have said that causes problems. I thought about sending some batches of mutt eggs to people by UPS 2nd day air or 3 day select and seeing how they hatch.
All USPS "Priority" shipments go by air also, so if plane is no good for eggs carrier does not matter.
There is no "best" way to ship eggs.
Or there is?, put them on a pillow on the back seat of your Cadillac or Lincoln equipped with air shocks, and drive to destination.
Only long distance Priority Mail packages would go via air.
And the best way to transport by car is to hang the eggs in a net from your auto ceiling so they do not experience lots of vibration. The next best way is in a bucket of sand on the floor in the back seat.
Not all priority shipments go by air. They try to send by ground first and only fly them if they won't make it in 2-3 days. However it was posted to a fish forum that frequently ships live fish that the priority mail packages that do end up flying are no longer placed in heated and pressurized cargo holds so if your shipping across country that would not be a difference between ups and usps.