We've had our fun with Zombies, Run! before. The fitness program/zombie horde simulator is one of the more innovative ways we've seen to get in shape. However, it's not all casual fun. Sometimes you have to get serious. If you're looking for an app to push you a bit harder, you may want to check out Zombies, Run! 5K Training. Currently on sale for $0.99 in the Play Store (75% off), this one gives you more in-depth structure to get you through a full 5K in 8-weeks.
The app should work much like the regular version, with audio stories to augment your running experience. As for the storyline placement, the new missions (24 in total) take place between episode 1 and 2 of the first season, and describe more of the training that your character goes through upon first arriving at the survivor's compound.
The New Year's sale is likely to end soon, so if you want to grab both the 5K and the regular version for a total of $5 (normally, they're $4 and $8 respectively), now would be the time.