I want to read fanfic but i only partway through season 1 and i don't want spoilers what do i dooooooo?!
1) Fic written before the release of season 2 will mostly be fair game, or have clearly marked spoiler warnings for events in the second half or the finale of season 1 (for the most part). Season 2 came out in April of 2013.
The Zombies, Run! page on Archive of Our Own will be the easiest place to sort by date, so I'd suggest starting there. To use myself as an example, I know only a couple of my AO3 fics have spoilers for anything beyond mid-season one, because when I was actively posting to the Archive I was still playing through that season myself.
That being said one of the fics at the top of the first ZR page on Archive of Our Own has a summary that could spoil the end of season 2 for you if you read it, so skim down quickly and try not to look directly at anything as you navigate back to the early end of the collection.
2) Have you been to the Zombies, Run! fanworks delicious page yet? There are spoiler tags that you can look for and avoid. And again, looking for older fic will help some. The fandom was very good about tagging posts with zrs2 if they contained season two content last year, so even if a fic looks safe you can double check by scrolling to the end and looking for that tag.
3) A surprising amount of fic is pretty gen. straydog733's dialogue-only radio mode ficlets tend to be thin on spoilers unless otherwise marked, a lot of AUs make only very sideways references to future plot developments. If you tread with a bit of caution there is a lot to read.
4) Technically the same as the point above, but I'm pretty sure facingthenorthwind's Jackoala AU is spoiler-free. (It's about Jack. If Jack were a koala. No, you need to read this.)
Any other suggestions, followers?