Anime means Animation.
I would go with something that is the pinnacle of Animation, in not only storyline, and depth, but also in the visual.
Studying to be an Animator, you cannot pass up a Studio Ghibli film. Mainly a Miyazaki film. That is what Anime should be about.
Steer clear of series for a little while and focus on movies, it would be the best thing, in order to give variety, instead of watching the a whole series.
Ghibli has a strong range of movies, and the best to start with would be either:
Lupin III: Castle of Caligostro
Porco Rosso
They both have a good range of comedy, action, adventure, and just are brilliant in animation quality.