What other insights from your client's customer base should you be looking for, before you...

The main insights you should be looking from a database of customers you've uploaded should be several things:

Demographics: Information regarding the customer database, age, gender, age-groups, lifestyle, relationship status, education level, and job title.

Page Likes: Information regarding top categories or other fan pages that people interact with.

Location: Region, country or city for your customer database. Language that they speak.

Activity: Device that they use to access Facebook and activity levels they have interacting with Facebook content.

Household: Income, household price/size/market value, spending methods, and habits. 

Purchase: Purchase behavior on several fronts. 

For this case study, you want to look at top categories, location, and spending methods that they have in order to better segment your next core audience.