Fullmetal Alchemist TV, Movie the Complete list, in order

Route one: the 2003 series. It ran while Hiromu Arakawa's manga was still being written, so the studio ran out of source material around the halfway point and built its own ending from there. It's darker, slower, and finishes with Conqueror of Shamballa, a movie that exists purely to close out that 2003 story. If you go this way, that's the end of the story, full stop.

Route two: Fullmetal Alchemist: Brotherhood. Made once the manga was finished, it retells the story from scratch and follows Arakawa's actual ending all the way through. It's also the better first watch if you've never seen either version.

You don't need to watch both. Pick Brotherhood if you want the story as it was meant to end. Pick the 2003 series if you're curious what a different writers' room did with the same setup, or if you already finished Brotherhood and want more time with Edward and Alphonse. Either one is a complete, self-contained watch.

Everything else here is bonus material tied to whichever route it sits under: Reflections is a clip-show recap from the 2003 run, the Premium OVA Collection and Brotherhood's own OVA set are DVD-bundle shorts with no plot stakes, and the 4-koma Theater is just gag comedy based on the spinoff strip. Skip all of it without losing a thing.

The one movie worth catching on its own is Sacred Star of Milos, a standalone Brotherhood-continuity story set partway through the series. Watch it after you finish Brotherhood. It's a fun side-quest, not a piece of the main plot.

At the end, here's the short version: Brotherhood if you're picking one, the 2003 series plus Conqueror of Shamballa if you want the road not taken, and everything else is optional.