Personally I don't read fic, but I think a chapter a week would be fine.

A week mirrors the pacing of the show and it means you have time to write future chapters, otherwise you maybe trapped releasing 13 chapters at once, finishing on a suspenseful moment then leave the audience waiting a month before another bomb of chapters is dropped. It may work for some writers that already have readers, but a chapter a week is a good way to build interest. A week spacing also means there's enough time for readers to consider the story but not so much time it's forgotten. Plus, a week means you have time to interact with comments where if you're constantly releasing can be lost a bit.

As this is your first time, you don't have a set schedule yet so follow your gut, experiment a bit, or listen to what readers say.