Wolfox

as expected... from a large series that's usually the case

there's really no point in trying to order it unless you're actually planning to work yourself hrough the whole franchise. If that's not the case just start with whichever one seems the most interesting to you. the most you'll miss out on should be foreshadowing or callbacks for the /Stay Night related stuff.

If you want to avoid reading the various vns/light novels/manga:

Fate/Zero first, it introduces the mechanics of the series best of the anime imo. Be aware that this and the next series are mutual spoilers for each other

Then watch Unlimited Blade Works because it's deeply intwined with Zero

If you don't mind waiting for the next one, you can watch the Heaven's Feel movies as they come out, otherwise watch them all at once as soon as the last one is out

If you have the stomach for it, watch the Studio Deen adaptation of (mostly) the Fate route, but be aware that it's hot garbage compared to Zero/UBW

Watch Carnival Phantasm and the Emiya cooking show if you like comedy

Play Fate/Extra and if you like that, play the rest of the Extra series (you'll have to read a summary of CCC since there's no translation as far as I'm aware) 

Watch the Apocrypha anime if you're enjoying the series. It's got a lot of fan favorite characters in it, though it's generally considered to be a weaker piece of media

Now is a good time to pick up Fate/Grand Order if you're willing to sell your soul. If you're attached to your soul, wait a couple more entries

If you liked Extra, watch the Last Encore anime, though be aware that it falls flat very quickly around episode 5

If you're in this deep, pick up Prisma Illya

If you didn't regret that, your soul is already bound for hell so you may as well play Grand Order

Once you've beaten all of part 1, you can check out the GO related anime