I'm not an expert at this but have recently done pretty much exactly the same thing. The way I set it up is that I have one class for several rows ( Users ) and one class for one row ( User ). The "several rows class" is basically just a collection of (static) functions and they are used to retrieve row(s) from a table, like so.
The level of abstraction you need for your processing and data (Business Logic) depends on your needs. For example for an application with Transaction Scripts (which probably is the case with your design), the class you describe that fetches and updates the data from the database sounds valid to me.
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