You're kind of asking the question that led to the advent of golden era advertising: What is "the big idea?" What is the hook, the story, the concept that draws people in to begin with?
Check out some of the broader histories of advertising. Stuff like the classic "Hey Whipple" book, or the works of Ogilvy. There are many approaches, because if there was some single sure-fire thing, everyone would be doing it... and then it would stop working.
There’s a book called “Hey Whipple, Squeeze This.” that is about advertising but centers a lot of its examples around the 64-85 Charmin Mr. Whipper ads. Long story short people absolutely hated those ads and it sold a ton of toilet paper for Charmin. This is unfortunately the reincarnate. They know exactly what they’re doing. Check out the book, it’s great.
If you haven't yet read "Hey Whipple" http://www.amazon.com/Hey-Whipple-Squeeze-This-Creating/dp/1119164001/ref=sr_1_1?ie=UTF8&qid=1456533531&sr=8-1&keywords=hey+whipple
It has everything you need to get started.
What you are up against is time. CD's and recruiters don't have time to sit down and read a script. Even if it's awesome. The quickest way to show that you are a smart writer is headlines. Pick brands and write hundreds and hundreds of headlines. Write so many that you end up having great ones to choose from. Cut that down to a book of 30-40 killer headlines. Even if it's just black helvetica and the brand logo at the bottom of a white 8.5" x 11" if the idea is good it doesn't matter. You now have something that can be consumed quickly, shows your writing ability, and doesn't have a design element. Then add in your short stories, and have your scripts in there to show you have those abilities too.
If you have any other projects you think show your personality add those in as well. I used to work with a guy that his whole book was just weird projects http://davidneevel.com/2010/08/13/the-disco-chainsaw/
Stuff like this http://www.toddlamb.net/Notes-From-Chris-meme
It makes you stand out as a creative interesting person.
In the end they also just want someone around the office that fits in with the culture and won't drive everyone nuts so don't be that guy.
PM me if you want any more info.