People have recommended The Cabin in the Woods, and it's a great movie, but I suggest you hold off watching it until you've seen a lot of other horror movies. It relies on you being familiar with the cliches and genre conventions for it to work.

Alien & Aliens The Orphanage The Shining The Exorcist Dawn of the Dead The Fly The Thing Ringu Halloween Silence of the Lambs Rosemary Baby The Others

Should see but not necessarily must: Village of the Damned

I don't know true classic horror, but would absolutely suggest John Carpenter's Halloween and The Thing as starting points. I still view them as two of the greatest I've ever seen. I would also put Alien up there (horror/sci-fi).

For recent ones, It Follows and The Ba-ba-dook were phenomenal.

As for Blair Witch... when I saw it in theaters, people were literally laughing at it.

I suggest Sinister: http://www.imdb.com/title/tt1922777/?ref_=nv_sr_1

I would add Phantasm to the list. Not necessarily the sequels, just the original.

Event Horizon