In general, an appropriate transit test should reflect the particular shipping environment which the product will be subjected to, usually determined by the size, weight and shipping mode(s). See my answers here: Are there standard vibration and shock specs for shipment of a product? and here: Vibration testing
In my experience, the best test spec is not simply selecting one of the published standards and going with it as is, though that will be much easier and may be a better place to start. The optimum test will be instead based on different components of established standards and should contain references those standards.
The ISTA standard contains a variety of protocols from which you can pick and choose based on your needs. If you are looking for a standard that's easy to understand and use, ISTA is it. You should review their guide here:
Another consideration is access to appropriate test equipment. How are you going to perform these tests? In general, if you have access to the equipment necessary to perform the test, you should already have the knowledge to select appropriate tests. If you don't, then you'll need to have testing done by someone who does and they should be able to advise you.
In any case, forewarned is forearmed. Knowing that you're shipping via a UPS type of carrier and not knowing the package dimensions and weight of your product, I'd suggest a test consisting of the following as a starting point:
- 24 hr Thermal conditioning (X units at -34C & X units at +66C)
- 10 pt drop test (height determined by pkg weight) Onto the bottom vertex of the carton which includes the carton seam. Each of the three edges radiating from that vertex. Flat on each of the 6 faces. (UPS)
- Random vibration (typically 0.52 gRMS) for 1 hour on each of the three axes with a vibration profile according to ASTM D4728, ISTA or ideally a profile developed from data collected by monitoring your particular distribution stream.
The above assumes that the items will be shipped individually, shipping a palletized load is a different animal.
As you suggest, the end customer might have their own standards or requirements to comply with a different published standard. In that case, I suggest that you have a dialogue with them about testing for shipping and handling and make sure that whatever tests you perform meet or exceed their standard and that they agree to any deviation from their standard.
Source: I spent 7 years testing and developing test standards for a wide variety of consumer product/packaging for shipping/handling via all manner of transport modes.