Merge zip code based polygons to create sales territories

I have access the full data set of the KML file shown here: http://ift.tt/1Lw5w58

Here's what it basically looks like: http://ift.tt/15VqZnu

It's basically a bunch of polygons that match (close enough) ZIP code boundaries. What I also have is a table that shows which zip codes go with which territory (i.e., a territory overlaps multiple ZIP codes).

I'm looking for a tool that I can use to merge these two sources together to create new polygons consisting of the group of zip code polygons that make up a territory.

Mapping is completely new to me, so I'm not even sure which tools I need to use. Any direction would be appreciated.

PS: I should add that ideally I'd like to avoid making a big software purchase.