Fate/Zero is best avoided unless you've experienced the third route of Fate/stay night, which itself is best experienced after you've at least viewed the first route (and I'd still strongly recommend the second route).
So to anyone who wants to watch Fate/Zero, I would either recommend reading the Fate/stay night visual novel, OR alternatively read the Fate route of Fate/stay night, then watch the Unlimited Blade Works anime, then wait for the Heaven's Feel film trilogy to come out, and then watch Fate/Zero.
Reading the Fate route of the visual novel is recommended and NOT the original Fate/stay night anime. While it is true the original anime was mostly based on the Fate route, it also spoils things for UBW and Heaven's Feel.
This may be useful. It isn't really recommended that you watch the first Fate/stay night anime because it mostly follows the first route while spoiling the other two, but not giving the full context that Fate/Zero is best viewed with.
With Fullmetal Alchemist, the first series (FMA) and second series (Brotherhood) start off [mostly] the same and deviate after a certain amount of episodes. However Brotherhood rushes through the stuff already covered in Fullmetal Alchemist. Brotherhood was based on the manga in its entirety, while FMA was based on the manga
while it was an still ongoing and so went with an original continuation when it caught up.
The first 28 episodes of FMA correspond to the first 12 episodes of Brotherhood. However there are slight differences in the plot before it. So any of these three options are fine:
-Watch FMA then watch Brotherhood. There are things I like and prefer about the original series even if it didn't follow the manga.
-Watch the first 28 episodes of FMA, then watch Brotherhood. Although you'll be re-covering some stuff you'll get more detailed episodes and additional storylines that still make sense within Brotherhood's events.
-Watch Brotherhood. Brotherhood makes sense without you needing to see anything in Fullmetal Alchemist.
For the films, watch Conqueoror of Shamballa after FMA, it's not worth watching unless you've seen that series. I would watch Sacred Star of Milos after Brotherhood. Sacred Star takes place somewhere in the middle of Broterhood -- I've seen one recommendation say you can watch it any time after episode 24.