I would probably avoid using a repeater if one of your goals is to have an admin page that shows all payments by all users. This is not because the repeater is bad for storing the information you want but it is not suited to aggregating values belonging to multiple posts (clients).
I would create a separate post type for payments that has a relationship field that connects it to the client. This will give you an admin page that shows all of the payments in one place. You can add filters and actions that will allow you to add columns (for example a client column) and sort and filter content on the page by these columns. There are a lot of tutorials and examples on the web for creating columns adding sorting and filtering to these columns.
