Well, there are two rights you need to seek - master and synchronization.
Synchronization rights are the rights to sync both the melody and lyrics to your film/tv show. The master rights are the rights to a specific recording of that melody/lyrics. This is why you encounter TV commercials which sometimes play a cover of a popular song. They obtained the sync rights to use the melody and lyrics, yet were not allowed to use an original recording - so they either found another version they could get master rights to, or they did their own recording with a band/musician which they contracted the master rights from.
For using a real song, this involves scouring BMI and ASCAP to find out how to contact the songwriter, and then investigate how to contact the personal, company, agency which owns the master recording rights. It can be an arduous process, so that's where production music companies come in great (the kind of music you are mentioning I believe).
Usually these licenses come in two forms from production music companies (which own the rights to both) - royalty-free(buyout) and needle-drop.
Royalty-free (buyout) means that when you buy, for instance, a set of production music cds or hard drive, your purchase cost includes unlimited snyc and master rights to those recordings for use in any film/tv. They do not have to be reported on cue sheets, and royalties are not paid to the artist. The money is made up front in the product sales.
Needle-drop (see: DeWolfe, et al) means that you must report, and pay for, the song you use and only the duration which you use on that specific film. This is how the company and artists make royalties. Instead of charging and upfront fee for a global non-exclusive buyout license, you are charged for your exclusive usage of a musical piece on a specific film edit. Meaing: when you buy the rights to this needle-drop production track, it can only be used in that one instance. Want to use it again in another film? It must be reported and paid for. This is the one place where buyout it great because it does not apply.
My suggestion is to seek non-exclusive rights (all media) to use the production music in question. Because if you tell them exclusive, what that means is you want to buy up the rights to this song so that nobody can ever use this song again. You will pay a hefty fee for this if not aware of what you are asking for.
As mentioned by Rene, best to contact the rep at the production music library/company and they can help you navigate the logistics and licensing costs.
Good luck! Music can be a minefield sometimes ;)