Select by location for the specified distance relative to you clients store location. Select by graphic with you drawing the the circle.
The population is a little more involved; obviously you'll need to obtain sound population data, (blocks, block groups, tracts, whatever granularity you choose to work with) and then geoprocess the population data into the zip data.
A word of caution; population data assumes a smooth distribution across the given polygon. You'll need to proportion that population to your zip polygons: what percentage of the original population polygon area is now in the zip polygon * population.....
see https://community.esri.com/message/257860?commentID=257860#comment-257860
That should just about do it....