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.
The original "Mobile Suit Gundam" trilogy (79 up to ZZ), "SDF Macross" and "Macross: DYRL" come to mind. It only makes sense, since a good space opera requires epic soundtrack. And those are the really big ones. Evangelion also has a very nice opening theme.