What are your top three recommendations for someone new to anime?

As far as series go: If you need a good time, Miss Kobayashi's Dragon Maid is a must watch; If you wanna get more serious, an epic space opera is also an important milestone, try Mobile Suit Gundam or Super Dimension Fortress Macross; Once you get used to anime in general, you can also try Natsume's Book of Friends.

As far as movies go: Just watch every Ghibli title in their release order. Start with Nausicaä, which is pre-Ghibli but still the spiritual first entry in the set.