Since Fate/stay night comes from a visual novel which has 3 different storylines for the same events, the 2006 anime called “Fate/stay night” and the 2015 anime called “Fate/stay night: Unlimited Blade Works” are both legit. Which means you can start with any, since there is no “original series”, the only original…

Actually I should inform you that Brotherhood is the only true Fullmetal Alchemist anime (the only anime that sticks correctly to the manga story) whereas since Fate/stay night comes from a visual novel which has 3 different storylines for the same events, the 2006 anime called “Fate/stay night” and the 2015 anime…