I am new also to filemaker but i will try to help. What i would do is create 2 databases. One with the personal info and one with the payment information. Connect them via a relationship. Then i would use a portal that would show up in the personal info page of that person. From this portal you can add records to the payment information database if you have this option selected when you create the portal. About the auto-increment number of payments it wont really be a problem because you can see all the payment history on the same page, so you can add it manually without error. This is only a little idea i had for you database. I am sure there are some better ideas to come along soon. Good luck!!
if you need more indepth instructions let me know and i will give you more information.