The short answer is: any order you like!
The long answer: We'd suggest that you start with Season 1, Mission 1 and go through the story chronologically. You can fit in any additional content wherever you like, but here are some general pointers.
Our 5k Training app is set between Season 1 Missions 1 and 2 of the main Zombies, Run! app. The story in this app largely has no impact on the main Zombies, Run! storyline.
Supply Missions all take place between Mission 1 and Mission 23 of Season 1.
Race Missions are set around the end of Season 1, but you can play these after you've finished the Season. You can complete a single race mission over multiple runs. You don't need to run these, though, as all the information will be revealed in Season 2.
Airdrop Mode & Interval Training take place sometime during Season 2, but standalone. These are only available to Legacy and Pro Membership subscribers.
Season 2's Side Missions are Halloween themed and are fun, completely standalone extras that do not have any impact on the story at all.
Each Season of Radio Mode is specific to its respective Story Mode Season, and will contain spoilers if you listen to them ahead of time.
PLEASE NOTE: We've added this timeline to the FAQ because we get asked what order missions should be played in a lot. However you don't have to play the missions in this order at all. If you want to start from the last mission of Season 3 and work your way backwards that is totally okay! If all your friends are on Season 2 then you can skip Season 1 and come back to it later. You should feel free to play missions in whatever way you like because the game won't punish you for not playing in a specific order.