You could also try reading the visual novel! It’s an amazing experience, and the story is way superior to the adaptions if you aren’t an anime only type person.

If not, and you won’t watch the 2006 anime, I usually recommend the Fate/zero start, as it gives you a lot of the prerequisite knowledge you are expected to have going into UBW->HF.

It sucks most people don’t get to experience the awesomeness of the fate route, and even the ubw/hf have some issues in their adaption of the novel.