Tony, great question.
The general approach is to determine an objective standard by which you can measure different groups. To get that standard, you have to step out of user experience and into business analysis. There are multiple ways to define business value of a group. Lifetime Value (LTV) is a solid one.
With a standard like LTV, you can define groups in many ways: web analytics segmentation, market research, user feedback, data mining, etc. It's perfectly valid to define and combine them using any or all the different methods. It's also a perfectly easy way to get overwhelmed. Start simple, and focus on behaviors instead of groups.
Management should have an idea of their target audiences. Pick one. Determine what behaviors (e.g., sales) meet which business objectives* (e.g., $$$). Work backwards, determining which behaviors lead up to those. Behaviors which contribute directly to $$$ are called macro conversions. Behaviors that lead to macro-conversions are called micro-conversions. (e.g., account creations).
See also macro and micro conversions...
Once you determine the value of the group's behaviors, you can measure the value of the group. Better yet, you can use the same process to measure the value of another group... and another... and another. Put each group's LTV in a spreadsheet, sort by highest to lowest, and viola! You have a prioritized list.
This topic can also go much deeper through fields like business intelligence. For example, you can apply predictive analytics to find new groups or adjust existing ones based on the most valuable clusters of behaviors. Generating personas around the new high-LTV behavior clusters can inform high value UX design efforts.
It's getting late and my brain's getting too glazed to proof this well. Hopefully it makes sense!
* I'm assuming that management's business objectives/goals are SMART objectives, if they aren't, there may be bigger issues than audience priority, and that's outside the scope of this post.