In addition to what Limnos said, you can have your own payment method associated with your Apple ID so that you can use Apple Pay and make purchases online. However, only the family organizer’s payment method can be used for Family Purchases. The exception to that is that any family member can redeem Apple Gift cards and pay for their purchase with the balance on their cards without having to use the organizer’s payment.
As far as I know, having your own payment method associated with your Apple ID should not matter with regard to the ability to share purchases. One caveat to my answer is that we all set up our Apple ID’s and payment methods before I started Family Sharing.