Well fate grand order isnt part of the main story but this is how many would start
1. Fate/Zero - a prequel to route 1 which is Fate/stay night 2006 of the main route
2. Route 1 of the main route - Fate/Stay night 2006 (many skip this because of the bad animation and story overall including me)
3. Route 2 - Fate/Stay night unlimited blade works (this ones really good) Remember to watch the prologue to this and dont watch the old version of it watch the one made by studio ufotable
4. Route 3 and the last route of the main route in the Fate series - Fate/Stay night Heavens feel which is 3 movies
After that you are done with the main route in fate now you can choose to watch whichever alternate universe of fate you want such as Fate/Grand order which has 1 series and a few movies theres also some games to it i think. You could also watch Fate/Apocrypha or Fate/kaleid liner Prisma☆Illya then theres also a bunch of other games and visual novels. I haven't finished it all myself since theres so da** much to the Fate franchise.