What sort of background and how does a person get a job choosing the
music that is used in commercials?

Who chooses the music varies. The director certainly has at least some
imput, but often the recording engineer does the deed, choosing music
from compilations sold for this sort of thing.

Kriswrite

Oh, at least where I come from, there are several other possibilities: 
- Campaign manager (or someone at the advertising agency). 
- Sometimes even the marketing manager of the product to be advertised. 
- And sometimes, the decision is on hiring a musician, and letting
them work it out with the creative team.

As a former copywriter, I can give you some insight. At the agencies
where I worked, it usually fell to the writer who had written the
commercial (TV or radio) to get the music done. For background music
for lower budget jobs, this would involve listening to music
libraries: recorded music licensed for commercial use, available at a
fee that depended on the commercial's usage (one market, many markets,
etc). For bigger budget jobs, the writer would decide what commercial
music production companies to invite to submit a bid for original
music, as well as, in many cases, a demo of their idea for the
commercial, for a modest fee.
In brief, usually it's the agency that decides the music: the writer
or the writer/art director team.