A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
You can use Excel as a data store, but even a modest business requires quite a bit of thought when setting up a database. You'll need a separate tab with a workbook for each table.
Microsoft has a very simple example database called NorthWind that helps you learn the basics of making a relational database (which is what you really need here). Here's a screen shot of just one table from NorthWind in Microsoft Query on the Mac:
You will need to customize your own database with the columns you need. You will need a transactions table. You will need to track billing cycle begin and end dates. You will need queries to generate a report that has the transactions made for each customer during the billing cycle. You will use Word Mail Merge to generate your invoices.
There is a tutorial to get you started here:
http://www.agentjim.com/MVP/Excel/2011Relational1Intro.html
Most businesses wind up using a commercial database product that has a lot of the core work already done. Nevertheless, this is a very do-able project in Office for Mac should you want to take the time to really learn how the applications work with each other.