It would be best to watch at least one of the main shows first, just to understand the lore and setting, but there won't be any direct plot tie-ins or anything like that.

If you do want to just watch one show for the background, I'd recommend Fate/Stay Night Unlimited Blade Works if you like more shounen-y shows, or Fate/Zero if you prefer darker and grittier shows, with heavier themes. Either one works fine as an entry point.