With regard to "Do all Apple Phones support Apple Pay",
The list of devices that support Apple Pay are listed on Apple's support page
Essentially, it is:
- iPhone SE, 6, 6S or 7 (plus anything new that comes along)
- iPad Pro, Air 2, Mini 3, Mini 4 (plus anything new that comes along)
- Apple Watch
- Macbook Pro with TouchID or a 2012 or later Mac paired with an Apple Pay enabled iPhone or Apple Watch
iPhone 5 and 5S are the notable omissions from this list (although I believe that iPhone 5S can be used if it is paired with an Apple Watch).
More importantly, just because the device is Apple Pay capable, it does not mean that the user has enrolled a card into Apple Pay (It may not be supported by their financial institution or they just may not want to use it).
As to "what is the best way to approach this?" - This is subjective and is off-topic.