Q:

How to add radius to map of over 32,000 zip codes

I'm incredibly new to creating these types of maps, but I'm trying to create a coverage map not unlike the cell companies show their coverage.  Our database simply has lists of ZIP codes that our service covers and I want to display these on a map, colored in, like the cell phone companies do. 
I have figured out how to do this on my own (using QGIS and joining my CSV list with the shapefile from the USPS of zip codes)... But the thing I can't figure out how to do is to show a radius around each zip coded area.  Our coverage extends 100 miles (50 miles in each direction) from the center point of each zip code. 
With a list of over 32,000 zip codes, is there a way to easily extend the coloring area around each zip code to include this extra area? 

A:

"show a radius around each zip coded area.  Our coverage extends 100
  miles (50 miles in each direction) from the center point of each
  zip code." 

Convert your Zip Codes to Centroids.  Vector - Geometry Tools - Polygon Centroids. 

Buffer the Points.  Vector - Geometry Tools - Buffer

Some things to consider. 
Use a projected coordinate system that is in meters then your buffer distance will be 885139 meters.   I would suggest SR-ORG:7301 as you are working in the USA and desire a unit that is stable (ie not degrees).