CTD Futures Bond Delivery

Can anyone please explain this? At initiation, I understand buyer agrees on a purchase price; However, I understand that there is a basket of potential bonds that deviate from the underlying which the future seller can choose one to deliver. What I don't get is a. Why the invoice amount (cash outlay) that contract buyer gives to seller is actually not the initiation purchase price b. How is the quoted futures price calculated? And then c. I've seen some readings that say that related to part a. there is a credit / debit to make the total price paid equivalent to the initiation futures price. I have read Hull but can't seem to connect these few points. Thanks.