The short answer is; any order you like!
For the long answer, generally we'd suggest that you start with Season 1 Mission 1 and go through the story chronologically, but we have specifically designed the app so that you can jump about to any season and replay missions if you want to.
A lot of the different modes in the app overlap with each other, so we can only give the timeline in general terms. Season 1 is the start of the story, and Supply Missions all take place between mission 1 and 23. Race Missions are set around the end of Season 1, but again you can play these after you've finished Season 1. All of the information contained in the Race Missions is revealed throughout Season 2 however, so you don't have to play these if you don't want to. You can then move on to Season 2. Airdrop Mode and Interval Training Mode are both set during Season 2, but they are both designed to be stand alone modes, so there is no specific time to play them in Season 2. The special Halloween Missions (Side Missions S22, S23 and S24) are fun, stand alone extras which do not have any impact on the story at all. Once you've finished Season 2 you can then go on to Season 3. There are no additional modes which relate to Season 3 content, so once you've finished Season 3 you can go straight on to Season 4.
Each Season of Radio Mode corresponds to its respective Story Mode season, so if you listen to Season 3 of Radio Mode before finishing Season 1 you will hear about characters you haven't met yet.
If you also use the Zombies, Run! 5k Training app then the story in this app is set between Missions 1 and 2 of the main Zombies, Run! app.
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.