I don't understand why people make the Fate franchise seem so complicated. Let me explain it very simply in this thread, without spoilers, and you can decide on your own from which point you want to watch the series.

First of all, the universe of Fate is simple; there's mages and mages can use magecraft. Magecraft is a little different to Magic, but that's not important for now.

A bunch of mages formed something called the Mage's Association and they are in constant battle with the Church.

Why they are battling isn't important.

So three mage families, in effort to recover lost "true magic" (what it is and why isn't important for this thread) and invented a system. The Holy Grail War.

The Holy Grail War (HGW) is basically a battle royale.

In every HGW, 7 mages are selected to become masters, and they summon 7 powerful beings each, from the past, present or future to become their warriors, known as servants. Each servant is of a specific class.

The victor of the HGW, both master and servant, are promised to be granted any wish they want.