I'd start with the classics: Vittorio De Sica, Fellini, Rossellini, Dino Risi, Mario Monicelli
Umberto D. (one of the saddest movies ever)
Miracle in Milan
The Bycicle Thief
Amarcord
La Dolce Vita
Giulietta Degli Spiriti
I Mostri
A Difficult Life
The Easy Life
Operazione San Gennaro (found this one particularly hilarious)
La Grande Guerra
I Soliti Ignoti
Il Vedovo
modern classics? There are few, but worthy
Paolo Sorrentino's Le Conseguenze Dell'Amore and Il Divo (Tony Servillo is the BEST italian actor)
Garrone's Gomorrah
Nanni Moretti's Caro Diario
ACAB and Diaz are two massive punches in the guts, also. Can't remember the directors, tho
and I wouldn't also miss two TV series about Italian gangs so good they really shouldn't be overlooked
Romanzo Criminale
Gomorra - La Serie
here you go, you can start with those. There are way more, but this should be a fine introduction for a neophite