I wanted to know: does Sahara give you a prize for buying a specific amount of her items, or does she give you absolutely NO award for buying her items?
Sahara gives you a random carpet and wall every time you pay for her services.
If you like, it can be considered that her "prize" is an unorderable carpet/wall from her private collection; it is not always guaranteed you'll receive her own work... Sometimes you get cheap, commonly found carpet and wall.
Unfortunately, you could buy her carpets and walls every week, forever and what you receive will always be randomly chosen.
To clarify, there are no additional items or rewards you can receive from her, even once you've completed her collection.
An excellent Animal Crossing New Leaf catalogue can be found here.
A good source/online guide to New Leaf can be found here.
Except for the wallpapers (for the papering of walls) and the carpets (for the petting of cars) that she bestows upon you, there is no further reward for purchasing Sahara's services.