What tools to use to figure out what "zone" a polygon resides in?

[LS1]

I have a polygon layer and 3 zones (from a central point). Zone 1 is 15 miles away, zone 2 is 25 miles away, zone 3 is anything greater than 25 miles. I need to generate a list of polygon id's with the zone they reside in. Some polygons reside in 2 zones but I only want to assign to 1 zone. Need help with the tools/process to use to accomplish this. I created the 3 buffers and overlay of the polygon layer but some polygons reside in multiple zones. How to resolve that and just place the polygon in the buffer contains the largest area of the polygon? Thanks for your help. 

[JoeBorgione]

You'll need to make a decision as to how to deal with those polygons that are in multiple zones  Take a look at select layer by location. You may want to first interactively select your zones, and use a spatial selection that selects those polygons that have their center within the selected zone.