A very simple advise, always listen to what Meryl tells you. She knows her thing
I'm not going to repeat what she suggested.
As for movies I recommend you Akira, Vampire Hunter D, Vampire hunter D: Bloodlust, Ninja Scroll, Street fighter II. And maybe the Fatal Fury OAV's, if you like fighting games and martial arts. Also watch out for Record of Lodoss war, be it either the OAV's, or the TV series. If you like stuff like LOTR, trust me, you'll like this
And last but not least, I highly recommend you all of the 6 Rurouni Kenshin (Samurai X) OAV's (but of course, much better if you can watch the series first and then the movies to undersatnd everything muxch better, nonetheless, I've watched them all without having watched the series and I think they're outstanding.)
since you said "essential" I'll mention what I think you should not miss:
-Akira
-Rurouni Kenshin OAV's (the first 4, which show the origin of Kenshin, the other 2 are actually the whole end of the series)
-Record of Lodoss War
-Vampie Hunter D and Vampire Hunter D: bloodlust (the first one is a classic anime, pretty old, but it's awsome, and the animation is pretty good having in mind the epoch, now, Bloodlust, is a recent movie, which, in my opinion, has some of the best quality any anime can give you. Quality in mainly art and action, which are unarguably good, although the plot can differ quite a lot from one person to the otehr, although IMO is awsome)